1) Set up a UPS account, so that you have a User ID and password, and apply for  UPS Access code on the UPS web site.

2) Configure VirtueMart's UPS Shipping Module under Store > Shipping module list, and also turn it on as a shipping option under Admin > Configuration > Shipping.

3) Be sure you've set up an address for your store under Store > Edit Store, so that UPS knows what address you're shipping from. (I use a fulfillment company to do our shipping, so I used their address.)

4) Be sure your products have weights entered.

5) Install the following update/fix to the VirtueMart UPS module:
http://virtuemart.net/index.php?option=com_smf&Itemid=71&topic=28381.msg80824#msg80824

6) If you still have problems, check to see if your web host has issues with proxy servers.