How do you auto-fit columns in Excel?

Double-clicking on the vertical line between the columns will auto-fit the column to the largest value in the column.   You can tell you are in the correct location because your cursor will turn into a cross with two arrows going left to right.  
If you want to resize all of the columns in the spreadsheet at the same time

• Select the entire spreadsheet using a CTRL+A or click in the box above the row number and to the left of the A that identifies the first column.  
• Once the entire spreadsheet is selected, double-click between two columns to resize everything.