This is nothing new. A good number of people make money, or at least try to make money, with this.
Idea is simple. You make websites for future events eg World Cup football, Olympics etc, do marketing, monetize website. These websites are time based, would probably earn you only around the time during the event.
I will try to explain different parts of the process. Not in details, in summary pretty much.
A budget of $ 20 per project would just be fine considering you know how to make a website. You have to get a domain and hosting. These days domains cost around $ 8 per year for generic.com names, hosting cost around $ 5 per month for shared hosting.
Getting Domain Name
A very important part of the process is picking the right domain name. Domain must have keywords IMO to capitalize from this process. If you can get type in traffic for the domain that's the best.
You should make a very simple website with information. Not big websites, something with 10-15 pages would be just fine. Make the header reflect the event with catchy banner. SEO should be in mind when you develop the website. Few things to keep in mind for SEO are page title, meta tags, h tags, internal links with keywords in title etc. A simple HTML website would just be fine in this case. Or if you want to use scripted websites for ease you can do that as well.
Best approach is mixing different listening sources. For example you can use Google AdSense along with affiliate links.
Do link building like you would do for other websites. Make some free blogs with links from articles pointing to the main website. During the time of the event or starting little earlier you can use PPC campaigns like Google AdWords to drive traffic to the main site.