To enable Screen Sharing, go to the Sharing system preferences, enable the Screen Sharing service, and ensure that your user account is allowed access. By default only administrators are given access, but you can add specific users to the list or select the option to allow all users. When done, you can select your Mac in the Finder sidebar of another Mac configured with the same iCloud account and then click the option to share the remote Mac's screen and open applications and documents on it.
Screen Sharing supports additional options such as synchronized clipboards and drag-and-drop support for file sharing. With these, you can drag files from the Finder in your current Mac to the screen sharing window to copy them to the remote computer. You can similarly copy files from your remote Mac. To use the shared clipboard option (enabled by selecting "User Shared Clipboard" in the Edit menu), copy any selected text or images on either Mac and the data will stream to the clipboard of the other. Then you can paste it by pressing Command-V.
Since OS X supports multiple user accounts, you may connect to your remote Mac when another user is logged on. In these instances, Screen Sharing supports multiple sharing sessions. In this scenario you are given the choice to either log into your account behind the scenes or view what the current user is seeing (with his or her permission). Note that for either approach, anyone sitting at your computer will see an indication in the status menus that you are logged on.
Finally, while Screen Sharing can be set up for your personal Macs, this service is not limited to your own computers and can be used to connect to any others on a local network with Screen Sharing enabled. Additionally you can request screen sharing access to a friend's Mac via Messages. (Yosemite now allows you to do this between two people with iCloud accounts. Under Mavericks you could do this only via a third-party service such as AIM, Jabber, and Google Talk.)
When chatting with a friend or colleague using Messages, you can click the Details button at the top of the conversation, where you will see options for communicating with your contact. One of these is a pair of overlapping rectangles, which, if available, will allow you to view the screen of your contact.
If you wish to only access your remote Mac's files and not deal with a potentially slow Screen Sharing experience you can do so by accessing your Mac's files directly. Provided you have enabled the File Sharing service in the Sharing system preferences on your remote Mac, when you select that remote Mac in a Finder window's sidebar on your current Mac, you will see the various default and custom shared folders appear, which you can mount and then navigate through to access the files you desire.
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