How do I fix the chain on the bike?

Generally speaking, all you need is a "chain tool". These can be purchased online or from any bike store. Two things to consider when reusing an old chain:

1) If the chain length is too short once you have connected it back on the bike, you will not be able to shift into the two largest diameter gears. The largest gear in the front of the bike is the "hardest to pedal", while alternately the largest in the rear set is the "easiest to pedal". For most uses, this combination is not required and you can save money if the second caveat below isn't in effect.

2) If the chain is worn (is flexible when you bend it side to side or is very greasy and looks rusty and old) and if this worn chain did not previously come from the bike you are attempting to install it on...the chain will likely not fit the gears teeth that are on the bike. This is because the smallest gears in the back (and front) wear along with the chain, so the spacing between the teeth is different depending on how the chain wears them down. This means, you may be required to install a new cog set (rear gears) at the same time as installing a new chain.

All these parts can be purchased at your local bikes shop.

The 2nd caveat is good but still a bit vague. IF you want to be a bit more techy......

The proper way to tell if a chain is "worn" is not whether it looks "flexible or greasy or rusty or old" or yucky!!! but to measure the chain length change from new.

If it's rusty and dirty first clean it in some solvent (eg. kerosene, diesel oil, turpentine) and if necessary wire brush rust off, and work any stiff links so it will hang straight not kinky. If this is all too much work then sure, buy a new one (but you'll probably also need new sprockets then).

A little maths is helpful:

A bike chain link is 1/2" long exactly, so 24 links should make up 1 foot exactly. Let it hang straight down and carefully measure the length of 24 links, or better 48 links (from a convenient place like the edge of a rivet to the same point further along).

If it is elongated by pin wear (it is not actually stretched) by more than 0.5% (1/2%) then it is definitely worn enough to buy a new one. If less than 1/2% elongated then it may be worth re-using. That is just my opinion and advice based on decades of experience.

1/2% of 1 foot is 0.06 of an inch, but what the $@&% is that???

1/2% of 2 feet is 0.12 of an inch, that is just under 1/8 of an inch, that's not too hard to read from a steel tape rule or similar.

In other words, if 48 links are 24 inches plus 1/8" long, the chain is "worn".

Or if if 24 links are 12 inches plus 1/16" long, the chain is "worn", although reading 1/16" is not so easy without better equipment such as a caliper.

You can buy a chain wear gauge which will tell you the 0.75% and 1% wear points, which are useful to tell when to replace a chain when the chain and gears are all working ok, which is not the question here. See http://www.parktool.com/product/chain-we... for one such gauge (I don't bother with them)

It's way easier to work in metric,

12"= 304.8mm exactly and 24" is 609.6mm exactly.

304.8 mm plus 0.5% extra is 306.324mm

609.6 mm plus 0.5% extra is 612.648mm

It's easy to read a tape to the nearest mm, so if 24 links are longer than 306mm, or 48 links are longer than 612mm and almost 613mm, then it's worn.

Go do it! :)