Markets are full of photographic opportunities thanks to the colourful array of produce and people that pass through them. However, they can also be a little daunting, especially in foreign locations but if you remember a few simple steps, you shouldn't have too many problems. These include asking to take close-up portraits, not getting in the way of those running a business and the most important but simple step: be polite.
Wide lenses will give you the opportunity to capture stallholders and customers in their environment while a longer lens can be useful if you'd prefer to shoot more candidly.
Try to avoid flash as not only can it be distracting, it can also spoil the atmosphere you're trying to capture. As indoor markets tend to be low on light this can mean working with higher ISOs but most DSLRs cope with this fine so you can still capture great low light imagery.
Leave the tripod at home as the legs will just get in the way of other visitors. If you find you really do need a support, find a flat, solid surface you can rest your camera on. It's also worth keeping an eye on your white balance as some indoor lighting can leave a coloured tint in your shots.
Capturing portraits of people at work or shots of those visiting the market, buying goods, is the best approach to take. Shooting candidly is fine but for portraits with impact, take the time to ask the stallholders if you can take some shots of them up close. If language is a barrier, try smiling and pointing to your camera as this will often get the message across. Always thank your subject and take the time to show them the result. It'll also help if you can learn how to say 'hello', 'please' and 'thank you' in the language of the country you're visiting, if venturing away from home.
If someone looks uncomfortable because you're taking their photograph make sure you stop and walk away and always read up on what's acceptable and what isn't and respect the views / practices of the country you're visiting.
Remember to shoot lots and often as lots can happen in a market. Switching to continuous shooting mode can help, but it's not essential, you could also try shooting from the hip if you don't want to draw as much attention to yourself.
When you do have the opportunity to work more closely, try a slightly tighter framing to see what results are produced. If you have particularly large stalls to deal with that have lots of produce between you and the seller this could mean using the power of a zoom lens to pull them to you rather than you moving your feet.
If you're making a special trip to a particular market do remember to check that it's actually open and it's also worth doing a bit of research to find out when the busy times are so you can either arrive at the same time or avoid it all together, depending on what type of images you're trying to capture.