We've been using Skype (with video) regularly since getting my Nexus three weeks ago and it works great.
At first I had a problem with the volume being too low to hear during numerous Skype calls.  I then downloaded the "Volume+" app from the Play Store apps and that solved the problem.
Before downloading the Skype app from the Play Store you have to download a camera app since none was included with the Nexus.  I used "Camera".  After 'Camera' is installed you can then download the Skype app.
If you Google "Nexus 7 Skype problems" you should find articles advising what problems people had and how they were overcome.