You need to call Disney Dining and ask to make an "Advance Dining Reservation" (ADR). The full number to call from the UK is 001 407 939 3463.
An ADR is not a reservation in the traditional sense. You will be asked to arrive around 15 minutes ahead of your ADR time and you will then be seated at the next available table for your party size. It works really well for an operation on this scale which has to allow for a huge number of "no shows". Holding tables would cause chaos.
If you can't get the exact time you're looking for, ask what else they have available around that time. They might have nothing available at, say, 8.00pm and 8.15pm, but have openings at 8.05pm or 8.10pm.