Decide if you want to pull the trailer with your current car or truck. If you have a medium sized car, you should narrow your search to smaller travel trailers. Small cars can only pull pop-up camping trailers. Make sure that your car has the right hitch. Your local RV center can help you install a new hitch if you need one. Look for a "fifth wheel" style trailer If you have a pickup truck.
Decide how much living space you will need. If the trailer is just for occasional weekend trips for you and one other person, a smaller one may be best. If you have a large family, or plan to live in the trailer for long periods consider larger trailers.
If you are looking for something a bit more comfortable than camping, a basic travel trailer or folding camping trailer may work for you. Consider some higher end option if you are used to sleeping in hotel rooms when you travel. Options can include a stand up shower, air conditioning, convection oven and even a whirlpool.
Ideally you should try out RVing before you buy one. Renting a travel trailer for a weekend is a good way to do this.
Like any major purchase, you should buy from a reputable dealer. If you are considering a private sale, see if your local RV dealer will do an inspection for you. Ask your local RV club for recommendations.