• vertical dropouts?
    If so, buy a single half-link and round file, choose your gear carefully, get a worn-in (i.e. pre-stretched) but solid 1/8" chain to the closest possible length, only a bit too short (you may or may not need the half-link to do this), and then file the dropout the rest of the way. You'll only be filing <0.25" (6mm) from the dropout so it won't really weaken the frame.

    wheels
    If you're really lucky and it's a very crap MTB you may have a screw-on freewheel in which case you can use Loctite and a BB lockring to do the job. If it's a cassette freehub, you might be better off swapping out the hub....
    I've heard of people jamming up the ratchets of a free-hub body with jb-weld, in which case you'll need a single-speed cassette adaptor.
    If the back wheel is of high quality you may also consider a Surly fixxer which cost about £40 (IIRC) and converts a shimano free-hub wheel to fixed.
    another potentially cheap fixed wheel option might be to get a cheap front wheel with disc brake bolts and swap out the axle/cones for the ones in your MTB rear wheel.
    Hope this helps - I've done the dropout filing, the BB lockring ghetto-fix, and also the front disc-hub-to-rear-fixed too.

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