I used to have almost yellow teeth after drinking 2 litres of Diet Coke a day for 30 years. It had got to the point that I was ashamed to smile because of their colour.
Not any more!
There is an initial outlay of about £15 for an electric toothbrush then replacement heads for it as needed. I personally use Braun Oral B Advance Power Toothbrush and it's on sale for less than £7 atm.
You also need a whitening toothpaste and whitening mouthwash. Totally up to you about which brand you want to use, but again, IME, it's worth paying for a well known brand than a shops own one... I personally use Arm & Hammer Advance White Baking Soda Toothpaste, 75ml
and Listerine Advanced White Multi-Action Mouthwash Clean Mint, 500ml
but I've used others in the recent past and I've found this is the best combination for me.
You need to experiment and find what works best for you.
Brush slowly and carefully every day - if it doesn't take at least 5 minutes to brush your teeth then you aren't going slowly enough - don't forget those back teeth too!
After a week or so, maybe more, you will start noticing the colour changing very, very slowly.
When you've eventually got white teeth, keep using your combination otherwise the whiteness will fade again.
I know it seems like it'll take forever to achieve white teeth with this method, but it's worth it in the end and so much cheaper than forking out hundreds with a private dentist because it isn't available on the NHS!
It's also better for people who are phobic of dentists (like me) because it doesn't involve any visits at all.
Give it a try and be patient... you'll get there in the end!