Are there any simple tips to improve the SEO of a website?

Yes, one of the most simplest things that websites need, are good backlinks from high ranked websites. Social networks, Commenting on blogs, etc. Comment a few times on each blog posting your URL multiple times (no spamming, so read through the article first).

Here's a superb resource that could help you out better: Backlinko.com - the guy's an expert.