Whether it's a Farmer's Market - which pops up in your town once a week, a regular local Car Boot or Jumble sale, or one of the famous long-established street markets in London and across the country; markets are great fun to visit and BRILLIANT for photography  

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I love shooting pictures at markets, and because of my background with newspapers and magazines, prefer to shoot with a reportage or documentary mindset. Wandering quietly through the aisles or between the stalls and looking for interesting or amusing images. Trying to be invisible so that my presence doesn't ruin the shot or alter people's behaviour. 
People Markets are full of characters. Interesting looking people who make their living buying or selling old furniture and pictures or cooking food for the hungry visitors. You do have to be careful when you are photographing people though, deciding whether you can get the shot without them noticing, or if you think that's impossible, deciding whether to ask them for permission. Market traders are famously camera shy - but some of them will say yes to a photo if you ask nicely. Most will be happy for you to photograph their stall even if they don't want to be in the picture. 
Be respectful though and don't shoot pictures if someone says no.  

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Portobello 

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Camera - set your camera up for fast shooting. Auto or P are very easy but Shutter Priority is better if you understand a little about how that works. Use Auto ISO or 200/400 ISO and a shutter speed of 1/250th or 1/500th sec to keep depth of field to a minimum. You don't want to have to think about settings - but need to just put your camera to your eye and press the button 
Phone - phones are brilliant for this kind of work. Make sure the lens is clean, and remember to shoot Landscape as well as Portrait format. Use the volume buttons to shoot in Landscape. Be careful not to zoom in too far. The most modern phones have decent zoom capability, but they will still pixelate badly if you overdo it. Much better to zoom with your legs and walk closer :) 

Tips 
1. Be respectful - some people won't want you to photograph them or their stall  If in doubt ask if you can shoot a picture. When they know you are student they will usually be fine with the idea.  
2. But don't feel you have to ask everyone before shooting wider shots. Photographers are allowed to take pictures of people in public spaces.