If you are starting with some guppies, here is a BASIC check list of equipment your will need.

A Tank: Preferably a glass box tank. Any size above 3 gallons is ok for guppies. A 5 gallon tank can hold up to around 7 guppies. A 20 gallon tank can hold around 25 guppies. A 60 gallon tank can hold around 79 guppies. (the wider the tank is = more fish in one tank). Always ask a shop keeper which tank is best for you and your fish keeping needs.

Filter: You will need some type of filtration in your tank - A simple but cheap UGF (under gravel filter) is all that is needed for a quick and easy setup - a UGF is a plastic plate that fits neatly into most tanks (of course under the gravel) and uses an air pump to push air through the holes in the plates, through the gravel and up a tube powered by a air pump - if you connect an air stone it will create bubbles (air stones are included with most UGF's) after the water is carried by the bubbles up the tube it will be released back into the tank with no debris that the gravel caught. 

ALWAYS read the instructions and follow them carefully, you can get UGF's from almost all aquatic stores, the smallest priced at £2-£4 so this is a great and cheap method of keeping your tank clean. Although you can get UGF's with starter tank kits, I do not recommend these. 

Heater: Guppies are freshwater tropical fish, this means they live in freshwater (not salty), and need a good amount of heat to survive. You will need some kind of heater thermostat which you can buy from all good aquatic stores, a thermostat is almost always combined with heaters. For a 5 gallon tank you will need a 75Watt heater, for a 20 gallon tank you will need a 120-150 Watt heater to significantly heat all of the tank... you do not want hot spots or cold areas in your tank. It is best to ask a shop keeper which is best for your setup. but please remember ALWAYS turn the electric off before you put your hand or introducing new fish to your tank.

Buckets: buckets are a good idea if you have to wash gravel or temporarily hold fish in while you clean the tank. It is best to have 2 of these, one for holding fish (and get them back in the tank a.s.a.p) and one for cleaning the gravel.

Nets: It is crucial to have mesh nets for catching/moving fish. Make sure you get one of these from a pet/aquatic store - some metals that they use may be harmful to your tank water.

Whitespot and fungus cure: It is quite handy to have a Ich and fungus cure as fish might get theses disease easily if they are not used to your tank. Ich is one of the most common of fish diseases, next to fin rot and fungus.

Other things you might need need:
Gravel (for UGF)  
Algae scraper 
Air pump system - for filter
A selection of suitable decor and plastic plants
A Hood light (make sure this is for aquariums)
A Gravel siphon
A residual Current Device (RCD Plug)
A stick-on thermometer for the outside of tanks or an inside one.