One thing to consider is the distance between the outside of the lock nuts. Traditional fixed wheel bikes have this size at 120mm. If your frame has this dimension then, allowing for chain line, a fixed wheel will fit into your machine.
If the frame is made of half decent steel, the rear drop outs can be cold set. Make sure that the drop outs remain square.
Talking of drop outs, you will need at least semi vertical drop outs so that chain adjustments can be made. Traditional fixed wheel bikes have track ends that are horizontal 'drop outs'.
You can't use a chain tensioner with a fixed wheel bike.
You will also need a single chain ring. These can be converted from a multi geared chain set and I would advise the purchase of suitable chain ring bolts for a single chain ring.
Chain line is very very important. It will probably involve a different sized bottom bracket and or chain ring spacers.
Don't do it for style as you probably won't enjoy it. Fixed wheel riding is a totally different way of riding a bike that uses different skills and a different mind set.
