You can clean the top with your normal car wash soap both as a first step and as maintenance once you get it really clean. Use a soft boar/horse hair brush. If you don't have one, I have used a kiwi shoe shine brush and it's worked perfectly.
If it's really dirty in spots, you will need a dedicated convertible top cleaner. Meguiars sells one that you can get in Walmart/AutoZone/Advance/O'Reilly's.
You will also need a protectant for it. I can't think of one offhand that's OTC, but that doesn't mean you can't look.
If you are not in a rush, and can wait a few days, there is a 303 kit that is great. https://www.amazon.com/303-30520-Convertible-Fabric-Cleaning/dp/B000A8JNF0
The plastic can easily be fixed up with Meguiar's Plastx, again, something you can pick up from Wally world and the like. Or add it it to the order from amazon. I like it because it's a cleaner/light abrasive, so it's gentle enough for using every other month without worrying about cutting through the plastic.
Good Luck!
Looks like a fabric top? This 303 kit will clean and protect it.
For the leather, it's likely coated leather, most cars are. The actual leather is coated with a thin layer of vinyl to protect it, which means leather conditioner does squat. For most cars I just clean with some murphys oil soap (use a sponge or toothbrush and work to a good lather) and then top it up with some 303 aeorspace protectant (same stuff I use on the dash).
I recommend this for leaks, http://www.amazon.com/303-30520-Convertible-Fabric-Cleaning/dp/B000A8JNF0/ref=sr_1_1?ie=UTF8&qid=1439255719&sr=8-1&keywords=3m+convertible+top+waterproof
Worked like a charm for my top. Repelled all the water.
I used this set of cleaner and sealant with a nice soft top brush on my Miata. It worked pretty well at keeping the top hydrophobic. Best to not let the snow or ice pile up and soak in.
The one I've always used is 303, since my Miata days. Works really well and it comes in a kit:
303 (30520) Convertible Fabric Top Cleaning and Care Kit - Cleans And Protects Fabric Tops - Includes 303 Tonneau Cover And Convertible Top Cleaner + 303 Fabric Guard https://www.amazon.com/dp/B000A8JNF0/ref=cm_sw_r_cp_api_i_ls8uFbYA1BC8J
Purchase these products they work great.
Did the same search about 6 months ago and found these products had good reviews.
I also picked up this brush to scrub the top after applying the cleaner.
The sprays work well. The brush does leave some hair as others have noted in reviews, it's not hugely noticeable but I wouldn't buy it again.