If your bike was shifting smoothly before the tune-up, just inspect your shift cables and derailleurs for wear and tear, drip lube into the ends of your shift cable housing, and lube your chain. Turn the pedals run the freshly lubed chain through its gears and then run it through a rag to remove excess grease.
If your chain jumps or misses shifts, check your cables for stretch. Give them a tug. They should be tight enough that you can't easily wrap your fingers between the cable and the frame. If they've stretched, loosen the Allen bolt that anchors the cable to the derailleur, and with a pair of needle-nosed pliers, pull the cable taut before re-tightening the bolt.
If tightening the cables doesn't fix the problem, the barrel adjuster on your rear derailleur can fine tune cable tension. Run the chain through your range of gears and pay attention to where it skips. Is it reluctant to move to a larger cog, or too eager to drop down to a lower one? Turning the barrel adjuster in whichever direction you want the chain to go should fix this. For example: If it wants to jump up to a higher gear before it should, or if it doesn't want to shift down to a smaller cog, turn the barrel adjuster clockwise (looking from the rear of the bike) toward the smallest cog. Small changes can make a big difference in shifting, so don't rotate the barrel more than a quarter turn at a time.