Installation of extensions is very simple, just click Install. Once the installation completes, new extensions show up in the Extensions tab, just like if it were manually loaded.
Once installed, extensions will be loaded automatically. Currently, there are only thirteen extensions in the BApp Store but that will increase over time.
As this version of Burp is a beta, you may run into issues loading extensions from the BApp Store. I found increasing the MaxPermSize as suggested does help with some errors loading extensions. I personally use the following in my .bash_profile to run Burp.
nVisium plans to submit extensions to the BApp Store and has high hopes for the future of extending Burp with this new feature. There’s also talk of a new web interface for Burp, which could make it even more powerful. With every release Burp keeps getting better and better, making the life of web app testers easier.
More information can be found here and here.