Although mandolins do not require the use of a strap unless the player is standing, most people just find it easier to play one with a strap, even while they're sitting down. The strap leaves their hands free to move around the fingerboard freely, without having to support the instrument.
Straps made for guitars are usually too big to use for a mandolin, so you should try to purchase a strap that is made specifically for your style of mandolin. Here is a picture of a strap that can be used for an A-Style mandolin
This type of strap has a hole in one end, through which you will put the end peg. The other end has thin laces which should be threaded under the strings on the peg head, ABOVE the nut. If they are above the nut, they will not interfere with your playing.
Attach your A-Style strap to your instrument and pull it over your head, so that the instrument is on the front of your body. The end of the strap that is tied to your peg head will come up over your left shoulder, run all the way across your back, and hold the other end of the instrument up using the end peg.
Here is a picture of a strap that can be used for an F-Style mandolin.
These straps usually have a hole at one end, through which you will put the end peg. The other end may have thin laces, or, like this one, may be used to form a loop. The laces (or loop) are used to lasso the curlicue on the top of the mandolin, and hold it tight. Place the strap over your right shoulder only. The instrument should be on the front of your body. The end of the strap that is tied to the curlicue will come up and across the right side of your chest, go over your shoulder and down the right side of your back, under your right arm, and back to the front, where it holds up the other end of the instrument using the end peg.
Some manufacturers have variations in their body styles which will prevent you from tying straps in this manner – if so, you will need to contact the manufacturer to find out how to attach straps to their instruments.
Finally, if you are playing bluegrass music, your fellow musicians will secretly consider you to be a sissy if you use anything fancier than a piece of old rope for a strap.