Problem with chain and gears

Wash, degrease and scrub the chain and derailleurs with a good degreaser (like Simple Green). Dry the chain and relubricate it with an appropriate bike chain lubricant (not oil or WD-40). Shift the derailleurs to the smallest chain ring and cog on the cassette (low front gear, high rear gear) and then loosen the cable at the derailleurs, pull the cables taut and reattach them. If the derailleurs still need adjustment, here is a procedure for it:
Flip the bike over (so you can pedal the bike manually while you shift) and shift the front to the middle chain ring. Shift the rear to the highest gear (small cog). Release the cable from the pinch bolt on the derailleur. Adjust the screw marked "H" on the derailleur until the jockey wheel on the derailleur is aligned perfectly over the small cassette cog. Set the cable adjuster on the derailleur to the middle of its range (find this by screwing it all the way in and then count how many revolutions it makes until it screws out completely. Screw it back in one half of the total revolutions). Reattach the cable and shift to the lowest gear (the biggest cog). Over-shift and hold on the shifter, then adjust the "L" screw on the derailleur until the jockey wheel sits just past the last cog. You have to hold the shifter to do this. Now shift into the middle gear (or one of the two middle gears if the bike has an even number of gears) and adjust the derailleur using the barrel adjuster you previously set to the middle of its range. Adjust it so that the derailleur is sitting perfectly over the appropriate gear. Shift up and down the cassette while pedaling and in every gear, reverse pedal (freewheel) to make sure the chain does not hop. Adjust as necessary until all gears are smooth.
Now the front:
Set the rear derailleur to the lowest gear (big cog) and the front to the lowest gear (small chain ring). Disconnect the derailleur cable. Screw in the adjuster for the cable tension all the way (this adjuster is on the shifter of a mountain bike or the down tube of a road bike). Pedal to make sure the chain is not rubbing on the derailleur cage. If it is, adjust the "L" setting on the derailleur until the chain moves by without touching the cage. Now pull taut and reattch the cable and shift the front to the big ring while pedaling. If it does not shift up well or completely, hold the shifter past its normal shift and adjust the "H" screw so that the derailleur allows the shift. Shift into the highest cassette gear and keep pedaling. The chain should not be touching the front derailleur's cage when you pedal. Adjust with the barrel adjuster until the chain moves freely without touching the derailleur cage.
That should be it, unless there is another mechanical problem causing the missed shifts, like a bent derailleur hanger or damaged teeth on the cassette cogs or a bad derailleur. If it is still problematic, come back for further information.

i hope this helps
-matthew