You can apply for ILR after 5 years of living in the UK. And after another year, you can apply for citizenship.
You must save letters from banks, utilities, council, and other official organizations. When applying for ILR, you'll be asked to provide evidence that you lived in the UK for 5 years (previously they only asked for proof for 2 years, but rules often change).
You also need to add your spouse to bills to have their proof too. This can often be done online (e.g., on Thames Water's website), or you can write a letter requesting it.
You also can't leave the country for long. The current limit is 180 days per year, but this may change. Working from another country is probably also inadvisable unless required for your job duties.
There are several paths to British citizenship. If you weren't born to British parents, the most suitable is naturalization. It's better to find out in advance which path suits you best and start preparing early. This section only covers getting citizenship when you already have ILR.
If you already have ILR, you can apply one year after obtaining it. But for citizenship, you need to have lived in the country for at least 5 years. That is, for citizenship you need to have lived in the UK:
For citizenship you'll need:
No active action is required from the referee, but you'll need to provide in the application:
That's quite a lot of personal data, so it's better to befriend a British person in advance.
Referees cannot be relatives to you or each other.
More details about requirements can be found in the official guidance.