There isn't much to add to the IPC explanation.
Your question makes it sound like you don't have much experience with printed circuit boards.
A thermal relief is used to allow easy soldering to through-hole components. A direct connection to a plane sinks much of the heat applied to the joint, and makes it difficult to solder without overheating the component and board.
Every component pad has some minimum copper annulus required to ensure both proper plate-thru of the hole, and to ensure mechanical strength of the solder joint. Those numbers are also called out in IPC publications. Your EDA software should have some library components where this part of the work has been done for you.
Once you have the annulus size, you need only concern yourself with the maximum current, and the reactance your application can tolerate for signal integrity. You can then chose the number of "webs", or radial traces you will use to connect to the plane.
From the above starting points, you just plug the IPC equations in the reference I gave you. The final step would be to simulate the pad in the appropriate signal integrity software to make sure it gives you the desired results.
If your application isn't signal critical, then just use four radials of about 10mils width, and annulus of at least 10mils around the hole. That will get you by for soldering purposes, but it probably won't do too well for fast or high current signals.
The bottom line is - this is science, you need the background to understand what you are trying to accomplish. There isn't any cookbook that will do the job for you.