As well as all the paperwork and vaccinations etc we should consider the welfare and comfort of our pets. There will be a lot of travelling involved and animals will be confined to the car for the duration of the crossing.
This, added to the journeys either side of the channel, will mean a long day in the car for them; so take plenty of water with you. A lot of dogs associate car journeys with going for a walk, which can add to the stress for you and them. Before leaving it is a good idea to take your dog for a decent walk to tire them out and relax them. Also try to plan your journey to allow time when you arrive at the port to walk them again and to go to the toilet before you join the queue for the ferry. Once you are in the queue your dog will not be allowed out of the car (unless there is a long delay) until you have left the foreign port so it is essential that he has been walked and toileted before you embark.
While you are on the Continent your pet will be able to live pretty much as if he was at home. However, you should remember that you will not, as it stands at the moment, be able to go from country to country without the correct documentation, which will vary depending on the border you are crossing and in which direction. So thoroughly plan your route well in advance. Animals take time to adjust to new places and routines. To help them when you go on holiday it is a good idea to take familiar things for your pet; beds, toys, chews etc for both the journey and the duration of your stay. Animals take time to adjust to new places and routines so try and keep to the same feeding times as at home. Animals' digestive systems also take time to adapt to new foods, so take plenty of their usual food, either enough for the whole holiday or enough to allow the introduction of new feed over three or four days. Similarly, take some of the new food home so they can re-adjust slowly on your return.
If your dog is on long term medication (e.g. for arthritis, diabetes, heart problems etc) take enough for the whole holiday. Insulin (for diabetic dogs) needs to be kept in the fridge so allow for that in your plans. You should discuss the medication needs of your pet with your vet when you are sorting out the paperwork for the trip.
On the subject of paperwork, under the present scheme the way it works is that from the first rabies vaccine your pet has, it will take a minimum of 7 months before you can bring your pet into the UK. Once you have achieved this you can come and go across the channel whenever you like, providing you re-vaccinate your pet as necessary.
So in summary: give your pet plenty of exercise before travelling, take some familiar things for him, take enough of any medication he may need, take ample supplies of drinking water for the journey, make sure you have all the right paperwork and tell him to look left before crossing the road not right.