To tighten the chain on the rear wheel of a fixed gear or BMX, loosen the axle nut on the non-gear side and grab the wheel near the bottom bracket and pull so the nut move toward the rear of the bike. With your other hand tighten the nut pretty snug. Then loosen the gear side, grab the wheel in the same place, and push the wheel toward the gear side. Tighten the gear-side axle nut pretty snug. At this point the chain will likely have proper tension, but the wheel alignment will be off, so loosen the non-gear side to adjust, then do a final tightening.

Now before you do this, pedal a few revolutions with the bike upside down or in a stand and see if the chain is sometimes looser and then tighter. Then, to make up for possible out-of-round freewheels, axles, crank spindles, and chainrings, pedal until the chain seems to be at its tightest point, and then proceed to the tightening procedure above. Otherwise the "loose" pedaling phase will be tight and the "tight" phase will be overtight. Better a chain too loose than too tight.