There are many steps to overhauling a cup and cone bottom bracket, so make sure you leave plenty of time. Unlike modern, sealed type bottom brackets, cup and cone bottom brackets can be regularly serviced, and If you're careful, will last a very long time.
This is a long guide, so you can choose to either watch the entire video above, or follow it in smaller chunks by clicking on the individual steps below.
Steps to Overhaul A Cup And Cone Bottom Bracket:
The commonest type of cranks are aluminium, with square holes that fit onto a tapered square section axle. A nut or a bolt pulls the crank onto the taper to jam it on. They usually need a special tool called a crank-puller or crank-extractor to pull them off the axle.
Some bottom brackets can be adjusted to tighten or loosen the bearing. Others are fit-and-forget, when they wear out the whole unit must be replaced. Some have cartridge bearings that can be replaced. Identify an adjustable bearing by the lock-ring on the left-side cup
Modern bikes usually have cranks made of aluminium, they are mounted on an axle made of harder material, usually steel. If there's any play between the cranks and the crank axle the soft aluminium will soon get worn to the point where it's impossible to lock the cranks. If the cranks are loose don't ride the bike.