Each tool, brush, filter, and effect in Photoshop has its own purpose in the world. There is no simple "learn this tool well and use it for everything" because different tools, etc. are used for different effects.
For example, if you like shiny slightly-3dish glossy buttons on your page (these were very popular a while ago) you would need to use some shadow, several gradients, masking, and maybe a little hand-jiggering with a brush tool. For a background you may just use a solid color or gradient with a textured/patterned mask.
Since there is no "one part of Photoshop" to learn, the best thing you can do is to become well-rounded by using the various tools. Browse around and look at all varieties of sites. Take note of features that you like, and then try to recreate them yourself. Often you can dissect the elements - does the object have borders, gradients, textures, light-sources, etc. - and recreate something similar.
At the same time, I can't hammer-home hard enough that there is more to design than just Photoshop. My recommendation would be to take a design class at the local community college (or whever) and get a feel for things like balance, colors, whitespace, etc. These concepts often make the difference between looking professional and looking like somebody's aunt (who, in this scenario, is not a designer by trade) edited a Geocities template.