Use Conditional Formatting with the formula,
=A1<TODAY(), where A1 contains your date.
You can use conditional formatting - there are 2 different ways to do this:
1:
Make one cell today's date. Do this by entering the formula:
=TODAY()
Then highlight all cells that contain the dates which you would like to turn red if they are prior to today. Then click on Format-Conditional Formatting. Under Condition 1, put Cell Value Is, then put "less than" in the next drop down, then click on the square on the right side of the 3rd box and select the cell with your date (should look something like =$C$1). Then click on Format and put in what you would like the cell to look like - click on the "Color:" drop down, and select red, etc.
The other way you can do this does not require that you put a date in a cell. Without making a "TODAY()" cell, highlight the cells that you want to conditionally format (just like previous example). Now again go to Format-Conditional Formatting. This time, instead of "Cell Value Is", select "Formula Is". Now here's the tricky part. In your selection, there should be one cell that still has a white background (it's the first cell you selected when you dragged to select all of your cells, and it should show up after you click on Format-Conditional Formatting). Noting that cell's address (ex: D4), put the following formula in the box next to "Formula is":
=D4 < TODAY()
Then format how you want (red text, etc.).
Even though you are only specifying D4, it will apply the conditional formatting to all of the selected cells.
Hope this helps,
Russell