One of the cool features on most Macs, starting back with Mac OS X 10.4 (Tiger), is called "Screen Sharing". It's one of the choices under System Preferences -> Sharing (SPS). I've included a few images (at the end) associated with this feature. I happen to have three (3) Macs: 10.5.6 (Leopard), 10.6.8 (Snow Leopard), and 10.10.5 (Yosemite). All of them can be setup with Screen Sharing activated, but NOT with Remote Management also activated. Many other web sites that discuss this feature use Remote Management, which gives you Screen Sharing by default, but is more complex to setup.
In SPS, you select "Screen Sharing" and fill in the Users you want to allow in the lower right corner list using + to add them, and - to remove them. Then click the "Computer Settings..." button to get the dialog box that allows you to set a password for making the connection. I tried some random made-up password, but it wasn't accepted, so I simply use the same password as the only User, myself. That worked. HOWEVER, although all three computers were set like this, I could only get the Yosemite's screen from the other two machines, and those two couldn't be reached at all.
Still, from my Snow Leopard machine, I could access my Yosemite screen, just as though I was on the Yosemite keyboard. As long as I stayed within the "Screen Sharing" window, it acted like my Yosemite system. I couldn't transfer files, but I've already got "sftp" for that via Terminal.
OK, so here's how you get to your server machine using the "Screen Sharing" app. With Finder activated, do "CMD-k" from the keyboard. That should bring up a "Connect to Server' dialog box, which you can cancel with the red-dot. The server address is needed. If you don't have one in the list below, then enter the address of your server like this:
vnc://192.168.1.3
That's a "Local Area Network" (LAN) address. In my case, it's my Yosemite system. Assume I'm doing this from my Leopard system. If this is the first time I've used this address, I click the + sign to save it in the list below so I can choose it from there the next time. I prefer to use LAN addresses, but you could Browse your network and choose that way. When you've got your Server Address filled in, click the "Connect" button. You may be asked to "login" as a specific user. Then, your server's screen should show up from your target machine. That's all there is to it. When you're done, I recommend you Close the window, which usually quits from the Screen Sharing app.
Of course, you can't access a machine unless it is fully awake, meaning it isn't "shutdown" or "sleeping" in some manner. With the Energy Saver panel, you can select "Wake for Ethernet network access", which sets the Power Management flag called "womp". On Mavericks (10.9) and above, Wake-on-LAN is only a partial awakening. The machine must be fully awake, with a defined Desktop window. So for my Yosemite system, which I could "wake" from my other two machines by just doing a Remote Login, I had to add a script that would fully waken the machine. Then I could use Screen Sharing. I called that script "wakesys", and you can get it from the link below, but you must make it "executable" [chmod 777 wakesys].
Here are the images: First, the SPS Screen Sharing panel:
Next, the Computer Settings dialog box:
Lastly, the Connect to Server dialog box: