Replacement should really only be performed by some one experienced in pvc pipe fitting as the health, pitch and placement of the fittings are an important factor in installation. The work can really only be done homeowners if they are confident and experienced in drainage and or plumbing work.
The Basic steps are as follows:
Remove the lid to the well and unplug the pump from power while replacing.
Find the check valve. It should be above the discharge 1.5″ (sometimes 2″) pipe leaving the pump. A black one is pictured on the right.
The check valve prevents back flow of all the water back into the well when the pump stops flow. When expelling water the pump must stop at some point, at this point there is still water in the discharge line. The check valve is a one way valve that stops the water from pouring back into the well. If it is installed in reverse it will block the pump from discharging.If you remove the check valve or cut the line above the check valve there will likely be about 1-2 gallons of water in the pipe that will pour out. Be prepared to handle that.

It is a good idea to replace the check valve if you are replacing the pump. They eventually  wear out. You will have to loosen the valve and or cut the pipe to get it out and remove the pump. It is easier to replace the valve with the pump removed from the well.

Remove the old sump measure its base to the threading of the discharge line. You need to compare the height of the output location of the original pump in case you need more pipe line for the discharge leaving the pump. Please shop at a local builder supply. The pumps at Lowes and Home Depot are horrid. (Actually most stuff is and they do not help local business. Being locally minded is a great benefit to our communities). 1/3 hp is good mix of power and efficiency. installing more than 1/2 hp will often place much more strain and kick / vibration on the pipes when the pump activates. A single damaged or bad fitting and the joint could loosen leading to a leak.
As noted above, if the port for the discharge line of the replacement sump is close to the same height as the original pump then you should be able to simply use the existing piping. Maybe grab a collar, or a short spot of pipe just in case.
Screw fitting onto pump, attach collar if necessary. Install the check valve (the correct direction). And let the PVC fittings sit for 10 min. to dry.
After about 20 minutes check service by running a hose into sump well. Various sumps have recommendations  for the height they like the float, and the floats are sometimes adjustable. Set the float to the recommended height.
Replace the lid. And done.