Turn off water supply first. Assuming you are talking about a kitchen sink (because some people don't know the difference between a sink and a wash hand basin!). The cold tap will be fed directly from the mains - so to turn this off you need to locate the stop cock on your service pipe. Turn off the hot water feed to the sink - locate a gate valve - could be anywhere but try the hotpress and turn this off.
Disconnect taps - there will be a compression type nut where the supply pipes join the tap tails. A flanged nut secures the tap to the sink. Might need a basin wrench to do this (special spanner which can be used in vertical position) - anyway it will usually be awkward!
Disconnect waste trap. Sink (assume stainless steel and not a Belfast sink) is fixed to worktop by clips - loosen the screws on these - may be 6 or more.
Sink should now lift out - but may need to be prised off if there is a lot of silicone under it to seal it.
Fitting new sink is the reverse process. Apply plenty of clear sanitary silicone to underside of sink where it will contact worktop. Apply the clips and tighten up. Fit new mixer tap with gasket under it. Fit the flanged nuts to underside -on tap tails. Now is a very good time to fit flexible tap connectors - abraided pipe with isolation valves at one end. This will save you future trouble id water has to be shut off for say tap washer replacement. Connect to existing pipework (use PTFE tape on the threads).Re-fit old trap or new one if old one damaged. Warning: do not be tempted to tighten the plastic ring with any kind of wrench - especially a Stilson - just tighten by hand only.
Open stop-cock and hot water gate valve. Check for leaks.
