"You just put the thing on the thing. C'mon guys, it's easy. "
Not a very helpful respones Fuzz.


The 2 racks you show have different methods of fitting:
The black rack you showed us is standard and will bolt into the threaded eyelets on your frame at the top of your seat-stays and at the bottom just above the rear axle dropouts. The correct thread for the bolt is M5. A threaded nut is not neccessary if the eyelet threads are in good shape but you do need a washer under the bolt head. Make sure the bolt does not extend too far into the chainline to interfere.
You need to set the horizontal adjustable stays to the correct length to achive a horizontal top.
At the seatstay eyelets, if the bolt goes INTO the farme tubing make sure it is not long enough to touch the opposing inside tube wall.

The 2nd rack with baskets that you show is attatched directly to the rear axle with the axle nuts holding it in place. This is not ideal, you have to remove the rack to remove the wheel. If your bike has a quick-release skewer type fitting with a hollow axle, you shouldnt attach this kind of rack to the axle, the wheel will NOT be fastened safely.

The holes in the rack-with baskets are much larger than 5mm. You could attatch it the same as a standard one but the large holes will allow it to shift around and you need to think about the correct size of washer to spread the load wide enough.

Which style of rack do you have?