A money order is basically a cheque, except instead of coming from your account, it comes directly from your bank (you basically give them the money from your account). It's more secure than personal cheques because it does not directly access your bank account.
If you're shopping online, what you'll have to do is let the seller know ASAP that you intend to pay by M.O. You'll need to know the final total amount (including all shipping costs) that you owe him/her, as well as his/her real name and mailing address. Once you have that, you go to the bank and ask for a Money Order in that amount, which you then have to mail to the seller. Some banks may ask for the seller's name and address for security purposes. Once the seller receives the M.O. and it has cleared/been successfully cashed in at their bank, THEN he/she will send you the item which you bought from them.
Now the risky thing with M.O.s, and a large reason why a lot of sellers (at least on eBay) won't deal with them, is the wait as well as the possibility that it will get stolen or lost in the mail. That's why they wait until they've received and cashed in the M.O. before they'll send the item. So if you plan on using M.O.s expect on having a longer wait time than you would have if you used a service like PayPal.