I'm a big fan of the function list palette, as a list of functions. Choose Insert > Function List and the palette of all functions will appear. Much easier to use than the wizard just as a reference. In the dropdown list at the top of the function list palette, select the category of functions you want to view.
Then just double-click the function you want, or click the little F(X) button in the palette, and the function and syntax will appear.
But look what appears, for instance, for =AVERAGE.

That's just not that helpful period; the average of one number is itself, plus who wants to find the average of a number?
If you look at the function wizard (click the F button next to the function entry field on the toolbar) or look at the help or do something else I'll show you in a second, this is the syntax. You could do a range or just list the numbers.
Likewise the syntax for =CONCATENATE from the function list is this
(not helpful, though not strictly wrong)
and the actual syntax that would be helpful is this.
Sometimes the function list does give you the full accurate helpful syntax as with HLOOKUP.
Here's what I recommend.
* Use the function list as a reference to jog your memory. Is it AVERAGE or AVG, that kind of thing.
* Then use the function wizard to get the real synta
* Or the help
* OR (fastest) type in the function as shown.
* First you get a popup with the name and the basic syntax.
* Press Enter. Then you see the full syntax.
* Don't press Enter, it will disappear. But you can use it as a guide to the syntax, and drag, click, or type to enter the appropriate cells/ranges/values.
Another approach is to use the function list, click to add it and its maybe-not-complete syntax to the cell where you want the formula, then click between the parentheses. The same little popup that you get with the previous approach will show then too.
The key point here is, the function list doesn't always give you the whole story on the syntax. Get the full story another way.