The NHS website will first ask you to confirm your date of birth.
You will then see a screen like the one below.
The page will display any sessions with appointments. If there are none (or the dates are not suitable), then click on the downward arrow on the left (circled above, in red) to show weeks further in the future.
If sessions are available, they will be displayed below. A "session" is a GP surgery - a morning or afternoon on a specific date.
When you have found a session on a suitable date and time of day, then select it by clicking on the arrow on the right (highlighted below, in red).
You will now be shown which exact times are available.
Choose one by clicking on it. You will then seen the full details of the appointment. Click "Book Appointment" to make the booking.
If you want to cancel or change the booking, you do this by using the link in the original message.