Well, that question is as big as the world around us. Sorry.
Sheldon Brown covers it fairly well with his articles and if you're not sick of being referred to them, you haven't read enough of this forum yet
But just to demonstrate what can be done pretty easily, I thought I'd show a few shots of my bike polo bike ... especially as it allows me to show off my bike polo bike
Here be the beast

Essentially, she's a really low end, el cheapo bike I bought off Ebay for $20. At that time, she had steel wheels, steel drop bars, rubbish cranks, low end 5 speed gears, low end brakes and ... wait for it ... 'safety levers' on the brakes (those extensions that come along the front of the handle bars).
She had everything taken off her, all the bearings pulled apart and rebuilt. I added some second hand track wheels (and promptly stripped the rear hub starting a race) and some rather nice alloy, track bars. I built her to give me an intro into track cycling and while she worked on the track, she was far too short for me - I could sprint like blazes but she weren't comfy in the slightest. Then our track career ended as my son started preseason training for his soccer club. So she got parked in the shed.
The beast she is now is my response to bike polo needs. On the surface, she makes a fairly typical 'fixie' for the road but there are a few modifications to make her more suitable for bike polo such as the low gearing (45x22 - it'll go lower when I change the chain ring), the brake on the back wheel rather than the front (yes, it is fixed) and the shortened bars. This is very much the Mk 1 version and will be modified as I decide it's needed/desirable/fun.
However, it does demonstrate what to look for in an old bike to do up.
The first thing to look for, are horizontal dropouts - those the the slots on the frame the rear axle sits in. Basically, you need to be able to move the rear wheel backwards and forwards so that you can set the chain tension. You can see them here on my bike. You can run a chain tensioner on a SS but not on a fixed gear.

Frame. Ride the donor and determine whether it fits you or not. Bear in mind that many fixed gear riders like a shorter reach than their roadies, mainly because they ride in a more upright position.
Check the donor bike for what will need to be replaced - in my case, I've replaced pretty much everything but at $20, it's a pretty cheap frame.
The quality of the frame needed depends on how much you want to spend and what you want to do. My Road Chief is clearly a plain gauge, some sort of steel frame ... but is surprisingly light for all that.
Wheels - well, you won't buy an old bike with track wheels (unless it's a track bike), so assume you'll be buying wheels.
Brakes. Use them. Preferably the donor bike's (even rubbish brakes work with new brake blocks) but a new set of Tecktro, dual pivot brakes will set you back about $65.
Handle bars - use the donor bike's or something else? Depends on what you want to do, but you don't have to spend a motza if you don't want to. The ones on the Road Chief are mtb bars I bought second hand for little and just pushed through the quill.
Brake levers - if converting from drop bars to flat bars, you'll need to buy different brake levers, but again, they're cheap and work with road calipers. The lever on my bike is a Deore.
Cranks - usually you'll just use what's on the donor bike. I bought those ghastly purple things of ebay for some stupidly cheap price ... and they're made of cheese so probably weren't worth buying.

What to look for in a donor bike?
Horizontal dropouts.
Frame fit.
What it costs to buy.
What you will want to replace and what that'll cost you.
What the total build is worth to you.
Richard
(to the bod who sent me the PM asking the question, feel free to 'out' yourself, but if you don't want to, that's cool too
