Hi Kim: I'm sort of a newby like you said you are and these are the steps I take to have a table as I like:
First of all click on the clear width small button in the inspector pane, whith the table selected.
Verify you don't have any cell with the "No wrap" option checked.
If you imported the table from Word, clean all the word code (level of effort: nightmare)
Then, with the table selected click on the ["px" width] small button to apply to the table and every cell the current widths.
Be aware that if you have narrow cells with a long word, the cell will widen to fit the word. Otherwise, this will work once published the page.
If you need extremely precise widths, generate a 4x4 red .png in Photoshop or whatever image editing software you are using, and create an empty row at the very top or bottom of the table, place the 4x4 png in every cell of that row, and assign to each .png the width of the cell it's in, by 1 px height. (I use a 4x4 size to be able to select and handle the little image easier than a 1x1 px). Once ready, re-save the red .png but now make it transparent.
Check the code and be sure there is not white space between the opening tag and ending td tags and the text, and there are no paragraph tags enclosing the text. If you need a line breack use "<br />" (or option-enter, on Mac) to generate the soft breack. The paragraph tag (<p>) will add white space over and below the paragraph.
There are many other settings that affect the widths: the cell spacing and padding and the predefined text settings.
As many posters say, CSS tags (divs and classes) are a better way to precisely layout a page nowadays, but the learning curve is heavy. Maybe is better for the rest of the world if you keep researching epidemics instead of learning CSS.