This app was mentioned in 9 comments, with an average of 5.44 upvotes
Don't use taxis. Use public transport/bikes/rental car. Taxis are way to expensive in Belgium.
EDIT :
Haven't really experienced any issues with the official mobile app. Does it's job, surprisingly not bloated, pretty good.
https://play.google.com/store/apps/details?id=de.hafas.android.sncbnmbs
If you won't have computer with you at the trip you can check train schedule with this app.
Edit: I am an andriod user thats why I gave you this link. I couldn't find AppStore link. If you are using IOS phone I know they have IOS app also I think you can find it in AppStore.
The NMBS-app if you ever plan on taking the train. I'd guess the apps for the buscompanies as well if you are into taking the bus: De lijn for Flanders, Tec for Wallonia, Stib-mivb for Brussels. Those are the apps from the companies themselves, maybe there is a better one that combines them all.
The KMI-app for superb weather forecast and rain-radar.
I also use 4411 to pay for car parking.
Last local one I have is 112-BE, for in case of emergency. It sends your GPS-location whilst calling 112.
Brussels has a metro system.
Brussels and Ghent have a very good tram system. All along the coastline there is also a tram that is a very good way if you want to travel along it. Antwerp has a tram somewhere too but they're the only ones who care about it. And legends tell about trams in Charleroi.
If you go to any of those places, you can plan with those lines in the back of your mind.
NMBS/SNCB is the name of the national train service.
In Flanders De Lijn does busses and trams.
In Wallonia TEC does busses.
In Brussels De Lijn does some busses and MIVB/STIB does metro, trams and many busses.
Use this website or the app.
Either should incorporate all available options for train+metro+tram+bus.
Alternatively you can go to the website of each of the above companies and use their own scheduler/planner.
I assume you mean Flixbus which is a private company that does very cheap transfer between very few cities within Belgium. It's mostly aimed towards international travel for tourists. I'll suggest not to use it because it isn't even that much cheaper within Belgium.
There is no alternative to something like how greyhound operates. We (and almost any European country) use trains to travel between cities and across the country. On shorter distances if there is no train line, there will be a bus. And within cities you use metro/tram/buss.
If you're under 26 there's a "Go pass 10" for €52 which is 10 single trips.
If you're under 26 and you're here during a week that it's vacation, there is a "Go unlimited" which is €15 for unlimited travel during a whole week (but you need a MOBIB card which is €5 extra).
If you're older, there is the "Rail pass" for €77 which is 10 single trips.
Very small use case for you but if you're going to travel only a few stations far there is the "Key card" which is 10 trips for only €23. It's aimed at people who only need local travel so limited to traveling no further than about 10km or so which usually is about 4 or 5 stations away.
If you're going to a very "touristy" place there also exist excursion passes for many places. They are all-in tickets with a 1 time price that include the travel by train/metro/tram/bus to the place and also including the entry ticket. So in specific cases, these might work out to be the cheapest option and you find a list of places/attractions here. For instance if you go to Pairi Daiza, it's good because it's the only reason to go to Brugelette. Or for the Antwerp Zoo because it's the only reason to go to Antwerp.
That's all for the train.
If you're going to spend a day in Brussels, I would advice the "Jump card 24h". It's €7.50 for unlimited travel during a day on the trains, metro, trams and busses within Brussels of all the companies that operate there. Note that it needs a MOBIB card so €5 extra.
If you're going to use busses a lot or spend a day in Ghent, you want to check out the day passes of De Lijn. €6 for 1 day, €12 for 3 days and €17 for 5 days unlimited travel on any tram or buss. That's for Flanders and Brussels. TEC prefers madness with only a French/German website but they have a "Horizon +" which is €8 for 24h if you have a MOBIB card, €10 without and €16 for 72h but only available with a MOBIB card.
Transferring times... There are no set rules.
It can be that a train is 5 min delayed and you have to wait an hour for the next one. But it can be that a train is 15 min delayed and they'll hold the connecting train for 15 min and make you feel like you are a VIP or a royal. General rule is to always have a backup to get you home and something to keep you busy while waiting.
Special mention is maybe to always use your travel date when planning a route. There are different schedules during the weekend and also during vacation weeks when extra trains for commuters don't run. Or in the weekend there are extra trains going to the coast.
There also isn't public transportation during the night except for Noctis (MIVB/STIB actually) in Brussels but it's only a very limited amount of stops and only until 3h. De Lijn has something they call night travel but it's hardly past midnight so it's almost not worth the mention.
Also, I would advice to never rely on the last train of the day. But if you did and the train gets cancelled or you miss the connection or whatever, NMBS is obligated to get you to your destination. If you see personnel around you, talk to them and they have to contact a taxi service and pay for it. If that doesn't work, they have to contact a hotel and pay for a night for you to stay. If you don't find personnel you can take a taxi and pay for it (get a receipt!) and afterwards go to the NMBS customer service to get a refund.
I have been a KU Leuven student for one year, so I haven't got that much experience. But here are my tips.
General:
Housing:
You can also look for apartments (or a "kot") in the villages around Leuven, particularly Heverlee since it seems that is a good balance for people who have classes in and outside of Leuven (I think this is the case for mathematics). It's also much quiter than in Leuven itself. Googling "leuven koten" will get you somewhere but be careful with what you pick (look at the neighborhood on google streetview for example). The best apartments and "koten" are found through word-of-mouth.
If you have the time: come visit before the start of the year to familiarize yourself with everything just by walking around.
Food:
In the Alma (student restaurant with multiple locations in and around Leuven) you can get unlimited fries and mashed potatoes with each dish and free water. Try "Het Koninginnenhappje" from the Alma, it's super unhealthy but so good.
Know where the Alma locations are.
Transport:
Get a crappy looking, decent bike with a good lock. Ones like these do a great job: http://hollandbikeshop.com/fietssloten/beugelslot/.
Buy removable lights and a luggage strap (https://www.bol.com/nl/l/sport-vrije-tijd/vrije-tijd-fietsen-fietsaccessoires-snelbinders/N/17991/index.html).
Look into all the different options https://www.delijn.be/en/ and http://www.belgianrail.be/nl have for people with your background. Also make yourself familiar with the train stations in Heverlee and Leuven. Look for nearby bus stations for where you live. Also get this app: https://play.google.com/store/apps/details?id=de.hafas.android.sncbnmbs&hl=en, it's great for planning any route, including bus routes, and allows you to buy your ticket online and skip the queue.
Get the Google maps app if you don't already have it.
University:
Get this app: https://play.google.com/store/apps/details?id=be.kulapp.mobile&hl=en, it's the unofficial app for everything KU Leuven and far better than the official one.
Most of the course material is found in the "Acco" (univerity-run bookshop) or with the student-associations of your campus (I think for mathematics it's "WINA", https://www.wina.be/?language=en). There are several "Acco" locations in and around Leuven. My student-association (Medica) is notoriously late with their deliveries so don't put to much fate in them. Get an "Acco-aandeel" (https://www.acco.be/en/user/accoshare), it will undoubtedly pay itself back quickly. Get as much of your books from "Acco" and as little from your student-association if it's anything like Medica.
All emails contain an English version underneath the Dutch version.
Get to know Toledo (https://toledo.kuleuven.be/), the official online KU Leuven platform. This is the app (warning: it's pretty bad): https://play.google.com/store/apps/details?id=com.blackboard.android&hl=en.
Knowing basic Dutch will get you a long way and other students really appreciate the effort. For example: https://www.duolingo.com/ (Warning: this is Netherlands Dutch, yes there is a difference.)
Nightlife:
"De Oude Markt"
Optional:
Learn to drive like a maniac on your bike.
Learn to type your student number blindly. You'll be typing it a lot.
Learn a few curse-words for those dirty "pendelstudenten". /s
If you have any questions, I am happy to answer them.
Surprising no-one mentionned it before; you can buy your ticket via the SNCB App.
Enjoy.
There are no seat assignments for national trains, and there's no limit to the amount of people that can book a train ticket, so don't worry about your trains selling out.
You just book a ticket from start place - destination (or a return ticket) for specific dates, and you can take the train on any time for your chosen day.
You can book your tickets in advance if you don't want to go through the hassle of buying a ticket in the moment, just make sure to have your tickets on hand! In all stations there should be ticket machines and/or ticket booths where you can get what you need. You'll get the option between second class (cheaper) and first class (more empty seats) tickets, and one way or return tickets.
If you're under 26, you can get a go-pass which is cheaper than a regular ticket, and sometimes there's cheaper weekend tickets too.
There's 3 main train stations in Brussels: Brussels North, Brussels Central and Brussels South. You'll likely be arriving in Brussels South from London. The names for the stations are slightly different in Dutch and French, which can be confusing, so make sure you're in the station you need!
North = Brussel-Noord / Bruxelles-Nord
Central = Brussel Centraal / Bruxelles Central
South = Brussel-Zuid / Bruxelles Midi
​
There's also an app for our national railway if you want it: https://play.google.com/store/apps/details?id=de.hafas.android.sncbnmbs&hl=en
Within Brussels itself there's easy public transport through tram, metro or bus which you can get separate tickets for: https://www.stib-mivb.be/abon_tickets.html?l=en this is a separate company from the railway.
Have fun on your trip!
I think you can also buy tickets through the app: https://play.google.com/store/apps/details?id=de.hafas.android.sncbnmbs&hl=en.