Just drag a transition from the Transitions panel to the intersection of two photos or clips on your timeline.
If you have several clips selected on your timeline, you can add a transition to several at once.
BTW, have you checked out my free 8 part Basic Training tutorials for version 11?
Please clarify what you are asking. My request is based on
There many possibilities for the default video transition from the Premiere Elements workspace. But, "Random" is not one of those default video transitions type choices.
Consequently, I ask:
1. Are you asking in general how to place one video transition between two adjacent Timeline clips in Premiere Elements 11? SG has given you a general idea on that for applying the default video transition. An additional reference for that is the Adobe document in your program's Help PDF
2. Are you asking how to apply the same default video transition for all clips on the Timeline. The detailed answer for doing that in Expert workspace would be to highlight all the clips on the Timeline for which you want that same type of video transition and then Timeline Menu/Apply Default Transition.
But, I suspect you are not asking either 1 or 2. What I think you may be asking is how to apply different (Random) transitions across the Timeline for your photo slideshow in one act. If that is the case, "Random" is not a video transition choice in the Premiere Elements 11 transitions. What you could do if this is at the core of your question is to create you photo slideshow in the Elements Organizer 11 where you can set for Random as the transition type in the Slideshow Show preferences and then send that slideshow to Premiere Elements workspace with the Elements Organizer 11 Slideshow Editor's Output option of Edit with Premiere Elements Editor. More details on that if necessary.
If I have read more into your question than you really asked, please excuse.