I have a trek too and there are some old posts on here when people gave me advice on changing gears. I was having a horrible time with my chain popping off - still happens occassionally but not as often anymore. User-error!
First, if your bike is new you will eventually need your cables tightened - which can cause gear shifting problems.
Second, to avoid having the chain come off, I've taken to putting the chain on the largest, inner-most ring in the back before changing to my smallest, innermost front ring. (I usually ride with the middle front ring.) This causes spinning at first but then I slowly move the chain to smaller and smaller rings in the back as I hit resistance going uphill. Then as the resistance gets greater, I shift to larger rings in the back. I also make sure to change to my small front ring before I'm actually going uphill, when I don't have resistance. I'm not saying this is the "proper" way to change gears. But it's what works for me and I have the same bike so maybe it's worth trying?
Once you're on the hill, hitting resistance, you don't want to change your front ring. So you have to do so before you start going uphill. If you try to change the front ring while on the hill, it will probably come off.
Third, I've personally had some minor problems shifting back to my middle front ring. Basically I have to hold the shifter longer than I would for changes on the back ring. (I think the only reason I have a problem with this is because my hands are small, not sure if you have the same problem.)
Hope that helps! Good luck!



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