How to change jobs in UK step by step ?

Hi , I have tried goggling and searching reddit but I was not able to find a step by step guide.

I have been with the same company for more than 10 years and I am at the point where I can continue growing only by changing companies.

I have two interviews set up and I will continue to job hunt until I will find the right opportunity however I am not sure what will be logistics involved if one company will consider my to be right fit .

Do I wait untill I get a physical contract signed by the company with the offer until I put my notice with the current company? Is there anyone that changed jobs recently and is able to explain step by step what do I need to do ? I assume things have changed since 2014 as I don't remember what steps I did at that time .

Thank you