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Here's a good article covering all the basics of the halacha.
I would also recommend Ice Cream Siddur as an all-around Jewish app. It includes Sefiras HaOmer as well as optional Omer Alerts based on halachik time of day (so you can have it alert you at the optimal time to count).
Here is a free siddur with English translation and some English instructions. It's the traditional text, so it may or may not be what they say in your synagogue. If you're not comfortable wearing tefilin, I can't think of a reason for why you should.
Edit: Link correction
This siddur has the text for that.