Once the case is positioned correctly for work, locate the holes on the motherboard and the holes on the case or motherboard mounting plate. You might want to hold the board just above the case motherboard plate and see which holes on the case line up with holes on the motherboard. 

Now gather your spacers, pictured below. Screw them in to the holes in the case or mounting plate that line up with holes on the motherboard. You can tighten them with a 3/16" nut driver or by hand. Some cases have small spacers that snap into place. With these, you push them through the mounting plate from the rear and they will snap into place. 

For the holes on the motherboard that line up with an eyelet hole on the case (a hole that is very long so that you can slide things in it), install a plastic stand-off on the motherboard. The stand-offs should poke through the motherboard and expand to keep them in place. The little disk on the other end of the stand-off will later be used to slide into the eyelet holes. If your case does not provide eyelet holes, do not worry about this step. Some cases use only the metal spacer screws to hold the motherboard. In fact, if your case doesn't have them, good. 

Now slide the board into the case. Make sure it sits on the spacers and that all the spacers line up with an available hole on the motherboard. If you have any stand-offs installed, make sure the little disks on them are placed into the wide end of the eyelet hole, then slid over to the narrow part, thus locking them in. Once the stand-offs are locked in, all spacers should line up. If you have a case with a detachable motherboard mounting plate, simply place the board over the previously placed spacer screws on the plate, and make sure they all line up with holes through the motherboard. 

Inspect the screws you will use to tighten the board down. If the head of the screws are too wide, and you think they might contac t any circuitry on the motherboard, place a plastic washer over each hole. I've had some ATX boards refuse to start up later because they were grounded somewhere to the case, probably by a screw. 

Tighten the board down. Install the screws into each of the spacers underneath, through the board and the washers if you used them. Tighten them down by hand first, then finish them with a screwdriver. Make sure you do not tighten them too much. You don't want to crack your board. Just make them snug so that the board doesn't wiggle around in the case. 

If you were installing the board to a removable mounting plate, install the motherboard mounting plate back into the case. On some cases, the plate is installed from the side. On these, you insert the bottom edge of the plate into a guide rail on the bottom of the case and then rotate upward. The top edge of the plate will contact the case, at which point you can screw it in or a spring loaded handle will lock it in. On other cases, the plate may slide in a different way, as from the rear. These plates are then easily removed later if you ever need to remove the motherboard. 

Double Check your work. Check to be sure that the back of the motherboard is not touching any part of the case or mounting plate. Make sure the slots and connectors line up with the holes on the back of the case. And definitely be sure that the board is rigid and tight. If you press down on the board at any point, it should not bend down.