The simplest way is via their web site: www.dell.com and select the appropriate support option from the main web page.
Whether you place on on-line or telephone call for service, you will need to know your service tag and/or service code number. Dell places these on a sticker on the side of the computer -- normally on the left side as you're looking at the front of the computer. On a laptop, it may be on the bottom.
Dell's warranty varies, but it's normally at least a year, and additional years can always be added for a nominal fee. In any event, have your credit card handy in case your warranty has expired.