Hi Cnowe,
Your purple flower is a Clematis.* I don't know which one as there are hundreds of named varieties.* If you want to know exactly which one it is, I would suggest you post a picture at Garden Web's 'Clematis' forum.* Most of the folks there really know their Clematis.* Their forum isn't set up like ours, so be sure to check the box that you want email notification of any replies.* Only the original poster who starts a thread can get email notification, so if you answer someone else's question or post on an already existing thread, you'll have to remember which thread and return to see if there are any responses.
http://forums.gardenweb.com/forums/clematis/?31292
Be sure to add your state and hardiness zone to your location in your profile so they won't have to ask.* Knowing when a particular Clematis blooms can also help with id.
How you prume a Clematis depends on which type you have.* Since yours is considered a large flower you have two choices to prune.* Here's how to prune them.
http://dialspace.dial.pipex.com/clematis/clemindx.htm
Is the red flowered vine the one in the background?* The flowers look apricot to me and it appears to be a trumpet shaped flower, possibly a variety of trumpet vine.* There are many vines with that common name, some are frost hardy and some are not.* Since you don't say where you live, I can't tell what it is or begin to narrow it down.
Newt
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.