Clicking on the Column Headings is fine once you understand how it works...
For example, say you have a View that is sorted by [Album]... If you click on the [Artist] column heading, it will sort it alphabetically A-Z by [Artist], but it remains also sorted by [Artist]. By this I mean... It sorts all the Artists together from A-Z. For tracks that have the same artist, it sorts those by [Album]. If you look at the indicators on the column headings, you'll see that they're numbered. Number 1 is done first, then 2, then 3, and so on (I believe it only shows the numbers up to 4 levels "deep" but it works further than that).
So, continuing the previous example, if you then click on the [Genre] heading you'd get a list where all of the Genres are grouped together alphabetically, then within each Genre you'll get an alphabetical listing of each Artist (well, each one that has at least 1 track categorized as that Genre), and then within each Artist, you'd get an alphabetical list of each of that artist's albums.
So, you basically want to click on the headings in the reverse order of how you'd like them to sort. So, if you want a list that is sorted with:
1. All the Artists together Alphabetically.
2. Then, within each "artist" the Albums grouped.
3. Then, within each "album" the tracks ordered by track #.
4. Lastly, if some songs don't have Track #'s they should sort alphabetically by track name.
You do it in reverse.... You'd click first on the [Name] header, then on [Track #], then on [Album], and lastly on [Artist].
Generally I find that if I'm trying to get fancy and have them sort more than 4 items "deep" it's much easier to use the Customize Current View dialog box that dcwebman described. BTW: There are lots of ways to access that dialog, but the easiest is to just select any file in the view you'd like to sort, right-click, and choose Customize Current View.
If you set up a system that you will use in lots of the View Schemes, you can save it as a Preset by clicking on the preset button.