Hi OP,
I am unsure whether you mean a sedation or general anaesthesia but both are used everyday in practices and generally go very well. There can be risks associated as with any medication administered, which will be fully explained to you from the veterinary staff.
Sedation is used in many procedures such as x-Rays to ensure a stress free approach and to ensure we can get all the imaging we need in one go and there is also levels to sedation. The level of sedation and what medications are involved will be decided by the veterinarian - for example if a dog is very very stressed for a visit we can offer medications to take 2 hours before a visit which offer sedative effects all the way up to injected medications which can go all the way up to “heavily sedated” just underneath general anaesthesia levels.
Some of the sedations will naturally just wear off and the animal can come around from being sedated naturally and others we can offer an injected reversal medication which counteracts the sedative medication. While your pet is under anaesthesia or sedation they are under constant supervision of a veterinarian and a veterinary nurse to monitor your dog, this will include vital signs, and monitoring the level of sedation administered, eye lubricant if necessary to ensure that your pet has no dry eyes and to keep the time of sedation down to a minimum to ensure maximum comfortability for the pet. Your dog will typically have an iv catheter to allow for the medications to be administered, which will typically include shaving a bit of the leg to keep a sterile field, following the sedation they will also be monitored until they completely come around from the sedative effects. Animals can still be a little sleepy afterwards, and their appetite may be reduced that evening but we would normally recommend offering a light meal (again your pets team will run through this all with you upon discharge on the day).
If your pet is going under general anaesthesia and not a sedation and you’re particularly worried you can opt in for pre-op blood tests on the morning of the appointment this is classified as gold standard care and can help indicate any issues that may arise (it is not fool proof) but it can give owners and vet staff some insight and peace of mind before any surgical procedures if there’s anything that may highlight an associative risk for GA. As I said previously, sedation and GA are used everyday in practices all over the world and are generally relatively safe and do tend to go well, I can appreciate it is incredibly daunting when it is your own pet on the table and when you speak to the team on the morning of admit I would voice your questions so the team involved can put you at ease, they will explain any potential risks and explain what they aim to find from the procedure-results etc and typically you will get a call in the afternoon to say your pet can go home and you should receive a discharge hand off with a vet or a nurse to explain how everything went, what to expect from your pet going forward.
Goodluck, and I hope DP is okay :) x