You're going to need a phillips screw driver and an allen wrench. You may also want to put your bike on a rack, a work stand or a trainer. Whatever your choice just make sure you can turn the pedals.
The front derailleur is shown below with two screws. The one closest to the frame is for the little ring. The screw farthest away from the frame is for the big ring. Note that the latter applies to the Shimano 105. If you're not using 105 go to the manufacture's website and download the manual for your derailleur.
Step one is to put the chain on the little ring.
Step two is to chain the big ring at the rear.
Step three is to tighten the cable at the shift lever. Turn the grey barrel at the cable clock wise.
Step four is to loosen the bolt which holds the cable
Step five is to check that there is one to three millimeters of space between the teeth and the derailleur
Step six is to adjust the little ring screw. Turn left and it will move towards the frame. Turn right it will go away from the frame. You want one to two millimeters of space.
Step seven is to go back and revisit the cable we loosened. Just pull the cable hand tight and tighten.
Step eight, chain the little ring at the rear.
Step nine, make sure there is one to two millimeters of space between the derailleur and the large ring. If needed turn the screw left and it will move away from the frame. Turn right and it will move towards the frame. Note this turning is the exactly opposite for the little ring.
Lastly chain the rear middle ring. Then test all your gears. If it's shifting smoothly you're done. If it's not shifting smooth you can increase the cable tension in step 3 by turning counter clock wise.
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