If you have to ask, then I'd say 'call a Plumber'.
If your replacement waste is a significantly different size, you may well have to replace the trap or even alter the pipework. Even if you don't, often those replacement waste/overflow kits are cheap and not the best quality, requiring some additional sealing in order to make them leak proof. Taking out the old one can sometimes be problematic, and cleaning up and then fitting the new one so that it doesn't leak requires a bit of skill and experience, for example throw away that crappy foam washer, it's good for nothing. Make sure the black sealing washer for the top of the trap isn't stuck to the end of the waste that you are about to throw out! Don't use oil based mastic ('Plumber's mait') on plastic parts, use a decent sanitary silicon (e.g. Dow Corning 785). If the retaining nut is the big, hollow type (for the basket strainer/plug) you may well need to make a special tool since even the widest screwdriver won't drive both sides of the slot at once.
Not to put you off doing it yourself, but either do your research properly or get a decent Plumber to fit it for you. Sinks that leaks smelly trap water into the cupboard below are a nightmare, sooner rather than later the chipboard units will swell and crumble, not to mention the horrible smell..
Sparks (the Plumber), May 2018
