Almost any Chess interface allows you to set up positions. For Windows you could for instance use WinBoard. You have the choice there to place pieces through right-clicking and selecting from a pop-up menu, or 'sweep selecting' by a right-click dragging down until you see the piece you want.
Chess Software
The software that you've seen on YouTube is almost certainly ChessBase. It does well what everything else labors to achieve. The only problems are that it is expensive (~$160 if you don't fall for the half-baked annotations in Mega; more if you do) and that it has a tendency to crash (it rarely loses data through crashes, and ChessBase respondes to emails with solutions to problems usually within a week).
DinoChess is my recommendation for the second.
I am a chess teacher at an elementary school and we are looking to purchase two things to aid instruction. I'm unfamiliar with most software, so I was hoping to gather some recomendations.
The first thing: we are looking for software to that enables us to post quick scenarios and then clear the board quickly, like the software you see teachers talking/clicking over on youtube.
The second: software that would help students learn the basics of the game vs. just playing the game. We would use it to put it on the school's student computers and the program may interact with the student.
Thanks in advance.