Search engine optimisation basically does not require any tools. But to do tasks quickly and smartly tools help alot.
There are 2 tools provided by Google that are 100% must when you do SEO on any website

1- Google Analytics
2- Google Search Console

Tools that can help you for good SEO for your website

Google Analytics

Google Analytics is basically a reporting tool that helps admin to see how his site is performing. If there is anything that you need to, you can take timely action.

Google analytics provides every kind of reports related to your website traffic, traffic, how many views, how many clicks, bounce rate (how many visitors came and bounced back), reigion of traffic, source of traffic, devices used by user, age of user, gender of user, and their interest. Google Analytics is that good that it will report you about what device your website user is using and even what is his screen resolution. Google analytics also tells you that how many visitors came to your website and what pages they have visited and how much time they have spent on each page.

I will definately recommend to must use this when you are doing SEO for your website or you can also

Search Console

Search console is a tool that helps admin to tell google how to optimise website for a search. You can do it simply submit a sitemap to search console. Sitemap is a document that includes all the URLs of your website and tells google about the structure oof your website. This process helps google to better understand your website.

You can use online tools to create a sitemap. The is a very famous website XML SITEMAPS that is free to use and it will create a sitemap for your website by just putting in a link.

You can also submit a request to Google to index your website pages using URL inspection tool in search console. Whenever you create a new page on your website or make changes to an existing page, just copy URL and paste into URL Inspection tool. Once URL is fetched click on Request Indexing. Indexing might take 1–2 week time to crawl your URL

Social Media Marketing

You can also use social media websites to make an impact on your website SEO. Social media is also a great tool to drive traffic to your website. Making engaging posts attracts audiance, and if audiance likes your content they will follow the link of your website. When you will get more traffic it will definately help you to do good SEO.

There are many free social media platforms available, I have mentioned top 10 best social media marketing platforms in my blog. Read this blog if you want to know about what social media platforms you can use for your business for free.