This is a great question and one I’m sure a lot of people are curious about.
I am a vet myself and see a lot of dogs with arthritis which owners haven’t yet noticed so its great that you’ve picked up on this. I’m sure it’s very hard for you to see your dog starting to show signs given that you have lost another dog to it recently.
In terms of what to expect- they are going to want to get a thorough history and preform an examination of you dog to assess overall condition, weight see if there are any areas of obvious pain, swelling, muscle wasting etc. They may suggest some blood tests and/or urine samples to evaluate your dogs organ function with a view to starting on medications. Some vets will do this straight away or others when the patient has perhaps been on medication for a few days or weeks. They may also feel it would be beneficial to have a series of x-rays taken to look at any joints they are especially worried about. Beyond that, some dogs benefit from having other types of images taken, for example a CT scan (which is a bit like a 3D xray), to evaluate further, but this would likely be done at a specialist centre which your vet would refer you to if they felt it was necessary.
Be very honest with your vet- tell them exactly what signs you have seen and what type of improvement you would like to see. Ask them what the plan would be if the first treatment you try doesn’t work or isn’t enough as its helpful for both us and for you to have a plan in mind going forward. You may want to ask about options such as acupuncture, massage therapy or hydrotherapy in your area. They may have suggestions as to what is available close to you.
Some practices or referral centres (hospitals) do offer specialist pain clinics and if this something you might want to attend then let you vet know about this too- we won’t mind if you say you want to see a specialist, that’s what they are there for!
It may be helpful to write things down before you go as it can be a bit nerve wracking and there can be a lot to take in at once! There are some downloadable handouts on our website which may be helpful to look at or take with you.
I would expect your vet to want to see you back a few weeks after you start any treatment to assess response.
I hope that helps!