Does your bike have a triple or a double in front?

I'll talk about shifting with a double. The principles are the same with a triple chain ring in the front, but you have a little more latitude to shift with a triple since you have a gear in front that is in the middle range.

The trick about shifting in general is
1 you do not want to do too much cross over. Cross over what is that? Say you are in your little chain ring in front (which is closest to the bike) and you are in the little cog in back (farthest from the bike) that is cross over. So, if you have 10 -11 speed in the back then if you are in your little ring in the front you want dont want to shift any further to the outside on the back than say the 5th cog closest to your bike and vice versa.

2 when you are shifting, especially when you are on a hill under a load, you need to think ahead and shift a little early - so that you shift to the lower gear before your bike gets under a lot of load from the higher gear going up hill.

This stuff becomes second nature after a while, but at first, it takes somes thought and you will make mistakes. Hang in there on the learning curve.

Try these tips. If they don't work, your bike may need to be re-tuned. What can happen if the bike shop did not try to stretch your cable, or even if they did, sometimes, the cable can stretch in the first few rides and then the shifting will need to be adjusted because the cable that pulls the derailleurs is loose.

Hope that helps.

the Spoke