Choosing a vet
Not all vets are experienced with small animals like hamsters. So you should ask your vet if he is experienced in hamsters or not and many of them will give you the name and address of another vet if they know any experienced one.
Scheduling and preparing
If the actual status of your hamster is allowing it, you should schedule a vet-visit in the evening when your hamster is normally active. This means less stress for him. In case of internal diseases you should collect a few "new" droppings and take them to the vet, to give the vet the possibility to start a proper research, if normal diagnostics couldn´t clarify the problem.
To carry your little patient you should use a "critter-keeper" with a bit of wood-shavings and a bit of nesting-material from your hamsters nest. Don´t use wire-top transportation-cages or cardboard-boxes, the different and unknown scents of other animals or the darkness inside a cardbox will cause extreme stress to your hamster and may increase the problem.
Veterinarians are normally billing you direct after the treatment. To prevent problems, you should ask prior for accepted credit-cards, cheques or insurance-contracts. They´re also selling the medicine they may decide to give to your hamster, so vet-bills can become very high very quickly. In that cases you should ask your vet for the possibility to pay by monthly rates. Most vets don´t have any problems with this.