How do I set it up on my Nikon D60 to use this remote?

The English manual (Spanish is also available) for your D60 is available free od charge from Nikon below:

http://www.nikonusa.com/pdf/manuals/dslr/D60_en.pdf

The shutter on the D60 can be released by self timer or remote (and of course by the normal shutter button). You're interested in releasing the shutter via IR Remote. An explanation of the shutter release Modes are contained on a single page (Pg. 54) of the manual and should be reviewed before going to the next page. The use of the IR Remote Release Mode is detailed here. Briefly, it states:

"Highlight Release mode in the Quick settings display and select one of the following release modes..." <table of choices & graphics>

You could select either Self Timer (10 seconds), Delayed Remote (2 seconds) or Quick Response Remote, but you're interested in one of the last two methods. The shortcut "Self Timer / Fn" button mentioned is on the camera body - between the lens and directly in front of the "D60" badge.

I hope this helps!

I assume you're referring to the ML-L3 infrared remote?

Select Release Mode from the Quick settings display. Select Quick-response remote. This will make the camera take a picture when you press the button on the remote. Well, almost. The same focusing and exposure metering delays occur as if you'd pressed the shutter release button.

You can also use the Delayed remote mode for group pictures. This gives you two seconds to hide your hand behind your back before the camera takes the picture.

By default the D60 will time out after one minute if you don't press the button on the remote. Custom Setting #17 allows you to set a longer interval.