Get a printed statement of your current savings to show the seller that you have enough money to cover the cost of the home and attach this statement to your offer. If you don't have the funds right now, give the seller a timeline of when you will be able to access the money. Usually, sellers are willing to accept an offer below the market price if it's a cash offer but don't low ball them too much, of course.
You would write up a purchase contract for the home you are interested in and instead of any financing contingencies it would be a "cash" offer. Most sellers will ask for a letter from your bank stating that you have the funds available to purchase the property.