The instructions I'm looking at (on how to roll over a 401(k) to an IRA) say that I should open a new traditional IRA account. I have one that I've used for a rollover in the past (it was created to accommodate the rollover). Is there any reason I can't use this same one for this rollover, or do I really need to open a new traditional IRA for this?
From the IRS's point of view, you can use an existing IRA. The instructions may just assume that the reader does not already have an IRA, and hopefully the benefits department knows how to set up the rollover to an existing IRA. All they should need is an address to send the check to and the destination account number (they may ask for more than that just to make sure everything aligns, but they shouldn't need to know if the account is new or not).
The best way to do the rollover is not by getting HR of your previous employer to do the rollover (as the answer you have accepted recommends) but to tell your IRA custodian that you have money in your now-dormant 401(k) account. Give the IRA custodian the details of your 401(k) account and tell it "Go get 'em, Bears!" and your IRA custodian will do all the work for you. Remember that the IRA custodian is eager to get its hands on new money and will do everything in its power to expedite the process, whereas the 401(k) administrator will be having money going out the door and has every incentive to delay for as long as possible. If you go to your IRA website, you will find detailed information on the process and links that will walk you through the process.