There are potentially a few different issues that can be encountered with brakes which are not functioning correctly, but more often than not they will fall under one of the following descriptions:
From time to time, if one brake caliper is working more effectively than another on the wheels rim, the rider will experience a sense of “sponginess”. In other words, the brakes do not feel like they are applying consistent pressure when applied. There can be a variety of causes creating this problem. The most obvious one perhaps is that the wheel may be buckled and offering less surface to the brake pad. Of course it may also be that the brakes pads have not been aligned properly, nor the caliper arms set up to offer even application to the rim.
You pull the brake lever and nothing happens. Or the brake strikes the rim but will not release. Check the brake cable housing – is it split or rusty inside? If so the cable will not be able to move freely and the housing must be replaced. As cables are not galvanised, it is recommended that you replace them also. (Of course if the cables are frayed you will have to replace them as you will not be able to feed them back through.) However, if you are able to/need to re-use the old ones then you must at least lube them well.
Another reason for sticky brakes are dirty or seized calipers. Generally, this problem is also accompanied by the lever feeling slack and floppy when you release it.
Brakes are Slack
You are applying pressure to the brakes and very little is happening. Most likely this is because the cable has not been properly tensioned. It could also be however that the cable is slipping through any fixing bolts on the caliper arm and the bolt will need to be tightened.
If the brakes are making a squealing noise – the kind where people turn and stare and hunch away from you slightly on the street like you’ve just scratched a blackboard with your nails next to their heads – its time to give the braking surfaces some attention.
Your first port of call is to clean all braking surface areas (rim and pads) with a mild degreaser (lukewarm and fairy liquid will do, or specific degreaser spray). You can go even further by sanding down the pads down to get rid of any stubborn dirt.
Finally, you can try toe-ing the brakes. This means that when the brakes are set up, the front of the pads are marginally closer (say 1mm) to the rim than the back of the pads. In general with modern brakes now it is not necessary to toe the brake pads. But you may use this technique as a last resort to prevent and horrible noises if you choose to.