You can simply buy a domain name and pay for hosting. If you choose to build it yourself, many sites offer a drag and drop building system. It's easier than you think.
If you don't feel confident building your own, there are people on Fivver and other similar sites that will build it for you.
I use to have a site that I built, and I will tell you it is a lot of work to keep the giveaways updated and archive the ones that have closed. Plus the people who are visiting will not necessarily click on other ads.
Remember you only want to build a site if you can make money from it. Typically, the people who are entering sweepstakes are thrifty and are only there to get something for nothing. This type of person is difficult to earn money from.