it depends if you want to do it half-assed or right. if your bike is really from the 80's then it should have horizontal dropouts, so you don't need a tensioner (as mentioned above.

half assed:
-remove deraillers and shifters (will need a screwdriver or two and maybe a wrench)
-buy/borrow chain tool ($25)
-pick the gear you want in the front and back, shorten chain as necessary
-ride

right:
-remove deraillers/shifters
-provided you have cranks with separable chainrings, remove all chainrings but the one you want to use. this will usually require a crank puller for mountain bikes to get at the smallest gear in the front. you will then either need to buy single speed chainring bolts ($10) or file down the ones you have (if done right it works just fine)
-a) assuming you have freewheel cassette, as the 80's had, you need a freewheel cassette removal tool ($5) and a large wrench. then you will need a single speed freewheel ($15). you will probably need to redish your wheel, which frankly should be done by someone who is experienced with dealing with wheels. you might have to pay for that if you don't have a buddy who can help
-b) if you happen to have a freehub, then you need the cassette removal tool ($5) and a chainwhip ($20) and a single speed conversion kit ($20). the plus side is you don't need to redish the wheel, the down side is you need the chainwhip.
-buy/borrow chain tool ($25)
-shorten chain to appropriate length for the gearing you have sellected
-ride

what it really comes down to is that the parts are almost no cost, but if you don't have the tools, that's what's gonna make up the budget.