It doesn't sound like your training was very thorough so I would definitely recommend maybe looking at doing some additional training as infills are quite important. You don't want to be wasting time and product removing and re-doing full set of nails all the time.
When I do infills, I start by filing off the gel colour I currently have on the nails to take it back to the natural hard gel. You then need to tidy up around the growth line so if there are any areas that are lifted you need to file above the point where it's lifted in order to cut that bit away. Never file on the lifted bit because you will just cause further lifting. If the client wants the length taking down, this is the time to do that because of course they will have grown since you did them. Once you've done all that you do need to push the cuticle back and prep the new bit of nail growth the same as you would if you were prepping the whole nail.
Once everything is prepped you then need to apply a small bead of gel right down by the cuticle to build up that gap whether growth is. You then need to brush over the existing enhancement as well to restrengthen it across the apex and across the growth line. Once you've done all that and cured, you then just file and shape as you would a normal enhancement and you're ready to go with your colour or however you are finishing the enhancement.
With gel enhancements you never need to really remove them. you just keep infilling them indefinitely.
If you do you have to remove the enhancements, they can't be soaked off, you have to file the gel down and leave a very thin layer, if you try to completely file the gel off, you risk filing the natural nail and damaging it so just file the majority off and leave a super thin layer on the nail and that will grow out naturally.
HTH xx
...jewels not tools...