Yes, the "command prompts" that open while starting an emulator are meant to close like that.
The following steps are based on Windows 7. I'm just kind of assuming you use Windows at this point, and I can't remember if the process is any different in other versions, but if something doesn't sync up I will try to find the answer for you.
First you will want to copy your "android-sdk-windows\tools" path directory. Hopefully you know where this folder was placed since you just recently installed it, otherwise you should be able to find the full path in your Android preferences in Eclipse (Assuming it was setup properly).
Now open up your System Properties window. The fastest way is to just hold down the Windows key and hit the "Pause/Break" button, which is near the top right of most standard keyboards. Alternatively you can right click on your My Computer icon, whether it be from the desktop, in the start menu, wherever, and click Properties.
Now, on the left side of the screen (For Windows 7 at least) you should see "Advanced System Settings" somewhere. Click on that, and in the window that pops up, click on the "Advanced" tab. Near the bottom of that window you should see "Environmental Variables". Click that.
The window that pops up should be divided into two halves. The bottom half should be labeled "System Variables". Scroll down in that box a little bit and you should see a variable called "Path". Select it and hit the "Edit" button below.
Almost done, I promise! In the "Variable Value" box, go to the very end of the line. It is quite long, so make double sure you are at the very end, things could get a little messy if you're accidentally typing in the middle of one of the other paths. At the very end, make sure the last character is a semicolon. If it is not, just put it in. Now paste in that file path we copied at the very beginning, if everything looks right hit Ok.
Now open up a command prompt and try typing in "adb" (Minus the quotes of course!) again and see if it works. Hopefully it will print out a bunch of commands and what not, at which point you can try the instructions in my other post and see if it fixes your problems, but if not post back and I will try to look into things a little more.