a set of adjustable spanners (wrenches) like this
you can get poor quality ones that will be adequate for occasional plumbing work, in supermarkets and hardware stores, a set might cost you about £12. A really good one could easily cost you that for one.
Wilkinsons have some quite reasonable ones, but they are sold individually, not in a set. If you are looking at some in a shop, you will find that the jaws slide smoothly and accurately in good ones, and are loose and wobbly in cheap ones. A good tight fit is better as they will not slip on a tight nut, and will not round off the edges of the nut. I would not let cheap ones touch my car.
You may also find a pair of water pump pliers useful. The jaws are adjustable to about three sizes. Cheap ones will do unless you make a habit of it.
you will also need some screwdrivers, probably pozidrive, but you can usually pick up a mixd set of a dozen or so at a good price in a supermarket or hardware store. Look to see that they are stamped "chrome vanadium" which is a special steel used for good tools. Not chrome plate. Nothing else will do (same as for regular spanners). Cheap screwdrivers are almost entirely useless except as ornaments and they will annoy you. Test that it is a precise fit before turning. Look for an "X" mark across the cross head, which mans Pozidrive. Older phillips heads do not have it. The wrong size, or worn, driver will damage the screw and the driver.
You will also need a roll of PTFE tape (very cheap, get plenty), usually white, the yellow gas tape is thicker. If you can find silicon grease, get a tube or small tub. It is not easy to find outside plumbers merchants.
I am sure you will find a how to do it video on Videojug.
Get a few spare washers before you start, and turn off the water and leave the tap open. When you take it apart you might find it has a brass cartridge inside instead of a washer. Unscrew the old one and take it to the plumbers merchant to buy an identical one.
Always put an old towel inside the bath or basin so it will not be chipped when you drop your spanner, and put the plug in firmly to prevent screws falling down the drain.