Drywall mudding tape wet under and over
You have listed the process correctly, and if you're new at this, then yes use pre-mixed joint compound (mud). But hopefully you used the regular setting-type joint compound on the first coat with the tape because it has an adhesive quality to bond the tape. Lightweight compound or "easy sand" does not and that's why it's easier to sand between coats, as it has no adhesive in it. 

First, with a new 3.5 gallon of mud you'll want to add about an inch of water (it will sit on top of the mud) to the bucket. Use the appropriate mixer and mix thoroughly until smooth with no lumps. Put mud on the joint (wide enough to cover the tape width), place your tape over the top and lightly press it in with your fingers flat. 

Using your 6" taping knife (putty knife) start at the very top near ceiling and run over the top of the tape embedding it flush against the surface, you will have quite a bit of mud squeeze out of the sides from underneath, and you can use some of it to go back over the top if you like, but keep it VERY minimal.

You are going to put a total of 3 coats of mud on. Don't make the mistake of trying to cover it all in the first coat. Remember, the objective is to not see the joint at the end, so don't use too much mud on your coats or you can end up with a big mess and a very ugly wall. Each coat you put on should be wider than the previous; knife sizes for the novice might be a 6" first, 10" second and a 12" for the last coat. 

Remember, it's easy to add more later than sanding off too much.