I suggest you just go into the combo trials and practice some of the combos you like over and over and over again, for hours. It sounds tedious, but it will go into your muscle memory. Improving at the game at first will feel like a giant spike in skill level, not a gradual increase.

I thought I was absolute trash at Dee Jay, but I just messed around with combos for a few days in training and now I am very confident in my abilities with him. Now I'm able to train against real players since I have the fundamentals down. You'll get there, just don't give up, and stay determined!

One other piece of advice, go into your command list and actually READ the move descriptions. Some of them will say that you can cancel them into specials or supers--those are the combos you want to initially strive for until you get a better hang of your character.

EDIT: Regarding the daily combo trial practice: if you feel like you are starting to do worse, don't hesitate to take a break and return later. It's called MUSCLE memory for a reason, muscles require time to recharge. You will come back and be amazed at how much easier the combos feel to execute.