If the domain name that you want is already taken then your best bet is to look at minor variants. For example, perhaps you can add another word to the name or you can switch one word out for another. Perhaps you can register it using a different extension, such as by using a ccTLD instead of the .com domain.
Another option is to hyphenate, so instead of using mywebsitename.com you could try my-website-name.com. Just be careful, though – the last thing you want to do is to cause confusion by having a name that’s too similar to someone else’s.
Finding the right domain name requires a little bit of art and a little bit of science. It also often takes patience and a lot of trial and error. But that’s okay too. Remember, the right domain name is out there, somewhere. You just need to keep searching around until you find it.