I suggest you download Twhirl as it's my favorite for twittering - it stays open in the background and refreshes often.
Using the Twitter site itself, or using
www.summize.com and doing a keyword search (such as virtual assistant) - you'll be able to find interesting folks to follow. You can then click on the teeny photos of other twitterers a user is following and follow them as well.
If you @ or 'at' at a twitterer, they'll see it in their twitter stream. if you try to DM them (direct message) which is private only to them - you can only do that from your twitter or Twhirl if they also follow you back. You simply enter 'd username your message' and it directs the message to them privately.
So - for example, if you signup for twitter then visit
http://twitter.com/virtuallin - you'll see the button to 'follow' me. I'll get an email notice and will follow you back. If you use Firefox, you can right click on any twit follower photo in my list and open in a new tab - then follow them as well.
If you're really brave, you can sign up for FriendFeed.com - follow me there, add your RSS feeds, your twitter handle, flickr, etc and have a 'lifestream' - it rocks!