Check the brake blocks
First thing have a look at the brake blocks, are they worn? If so replace them, your local bike shop will sell you the right things, remember there are different blocks for different rims; steel, alloy or now carbon. If you like the feel of the original blocks try to get the same again, but you can experiment with different blocks until you find the compound that suits you.
Replacing the brake blocks
With some brakes you can just replace the brake pad and leave the shoe in place, on a mountain bike if you do this, make sure the shoe is adjusted properly so that the pad presses flatly against the rim, blocks can “toe in” a little, this means the front of the block will touch the rim first, this makes for squeak free and progressive braking.
With a 5mm Allen key (older bikes may be 8 or 10mm nut) unscrew the old brake blocks and throw them away, bolt the new ones to the brake, with road bikes it is easier, you have to make sure the blocks don’t touch the tire and they are level on the wheel rim, it’s the same with a mountain bike, but they are more adjustable, you have to place the washers on the bolt so that the pad is level with the rim and not touching the tire.
Brake adjustments
OK, so your new brake blocks are fitted, what next? First check that the cable is running freely, this helps the brake release properly (see cables master class), are the brake blocks making contact with the wheel rim evenly? Are both the brake blocks touching the rim at the same time, if not you need to adjust the calipers, loosen the bolt at the back of the brake that holds it to the frame (on a road bike), either with a flat spanner or your hand hold the brake where you want it, so the blocks are at a equal distance from the rim, and then tighten the bolt again.
With a mountain bike, if one block touches before the other you have to adjust the little screw that tightens the return spring on that brake arm, this pulls the brake arm further away from the rim so that both touch at the same time.
Adjusting the pull on the lever
How big is your hand? Or how long are your fingers? This affects how much pull you want on the lever. Small hands will want the lever closer to the bar before the blocks start to slow you down, if the blocks are far away from the rim it takes more lever to pull the brake on, for big hands the cable needs to be tighter.
Every one is different so experiment until you find what you like. On some mountain bike levers you can adjust the reach on the lever to bring it closer to the bar for smaller hands without having to leave a large gap between the blocks and the rim.
What else can I do?
First keep your brakes clean and adjusted properly, regularly check the brake blocks for wear then adjust them or replace them and keep all moving parts oiled or greased (specially after rain), a bit of oil on the bolts of the brake caliper and on the bolts and moving parts of the lever. Your brakes are very important, look after them and they will look after you.