The best way is to set up the Unity Asset Server or a third party source control system, such as subversion.

Otherwise, it is difficult to manually manage without simply copying the entire project, as the Library stores references to various assets you have imported.

If you are just replacing scripts and some textures- you can safely do this manually: the best way is to overwrite them in the File system (OS), rather than in Unity. When replaced in the file system, Unity will determine that you have simply changed the file, and preserve the references. If you attempt to overwrite from Unity, Unity will by default rename conflicting assets rather than overwriting, and if you delete the old and then import the new, you risk losing references to the asset in prefabs and scenes.

If it's just you working on the two machines, you can probably use version control with them without a lot of trouble. You may want to see my question on version control workflow or other posts with the same tag.

A simple and cheap way is to install Dropbox (www.dropbox.com) on both computers and when Installing it, edit the location to be a common place on both machines. Like C:My Dropbox\

A free Dropbox account gives you at least 2 GB free online space.

After this you can create/move your Unity projects into subfolders inside your Dropbox folder and Dropbox will automatically sync files. Only downside is that Dropbox sometimes locks your files while publishing a preview and you have to close Unity down before Dropbox will be able to sync the last bits from your project.

But once the Dropbox icon gets the little green check mark, you are safe to close down and switch computer.

Im pretty sure you would go to the drop down window that says "windows" and click on the type of window you want and it will open the window in a seperate tab and just drag it across to your other monitor