Let's start with the easiest solution to set up: Messages. Apple's built-in messaging client includes a feature that lets you offer to share your screen with any Messages-using contact on your buddy list, as well as request that you view a contact's screen.
Screen sharing requires a few things. First, youll need a high-speed Internet connection on both ends. For another, both parties need to be running at least OS X Leopard (10.5). Finally, you'll need either a Jabber (including Google Chat) or AOL Instant Messenger account, and your contact will need to have an account on the same service. (Yahoo and iMessage accounts don't support screen sharing.) You can set up such an account by choosing Add Account under the Messages menu.
Make sure that both parties have “Screen Sharing Enabled” selected under the Video menu. You should see a green icon next to some of your buddies, with either a video camera icon or phone icon on it. Either side can initiate the screen sharing session, either by Control-clicking on the contact and choosing “Share My Screen with John Smith...” or “Ask to Share John Smith's Screen...", or using the same option under the Video menu (see Figure 1). You can also click the Start Screen Sharing icon at the bottom of the buddy list; it's the one with two rectangles on it.
Your contact will be notified that you want to share screens, and will be able to accept or refuse your request. Once the connection is established, Messages will also establish a voice chat, so you can talk to each other. If you're viewing your contact's screen, Messages will expand it to fill your display; your own computer will appear in a small window that hovers in one corner of the screen (see Figure 2). Your mouse and keyboard can be used to issue commands the remote computer. (In fact, both parties will be able to control that machine, so be careful, lest you end up fighting over the cursor.)
You can toggle back to your own computer by clicking the My Computer window, and the displays will swap places with the remote display appearing in the small window. Should you need to send a file to the remote computer, just drag and drop it onto the small window showing the remote computer. Either party can end the video chat session by choosing End Screen Sharing from the Buddies menu.