>>1515290if the bike is anything like the pic
most important of all make sure your cable housings have no kinks in them and have a little oil inside each end of them
many shifting problems are made worse by cable friction and rust
the derailleurs are an old design (same as shimano TY15-GS), crude and easy to adjust,
cheep Chinese Derailleurs have weaker metals and plastics, often they are a little bent and flexy
check the Derailleurs for alignment and how steady they hold the chain in line
if the Derailleurs are fine the next thing to look at is the shifters
the bike in the picture has twist shifters
made popular by SRAM and sold by them under the name GripShift
many clones of this exist and they are much worse than the original despite looking much the same so its a gamble as to how good the shifter is
a good brand of twist shifters is shimano Revoshift
they are a little larger and have a planetary gear set inside of them that makes the shifting action lighter
only down side is cost and they they are a little fragile
the bike in pic appears to be 21 speed (3 chain rings - 7 cogs)
good seven speed thumb shifters can be a little hard to find and by the time 7 and 8 speeds were common many of the shifters were indexed
http://www.fa-technik.adfc.de/Hersteller/Shimano/SL.htmljust what I have used and found to work are
Shimano SL-TY37 (light action)
Shimano SL-TY22 (a bit clunky but accurate)
some shift triggers also work well but are hard to find in working condition
http://www.fa-technik.adfc.de/Hersteller/Shimano/ST.htmlshimano ST-EF28- (old but good)
shimano ST-EF29- (slightly newer so not as durable)
newer shift triggers have more plastic in them that can tend to fail or let water and dust into the mechanisms
>fix the brakesa little harder than it sounds
in the picture is v brakes but the cheep kind that uses smooth post brake pads as found on older canter lever brakes
they have a wide range of adjustment so can be tricky to get just right