I am a few years out from undergraduate school so this primarily speaks towards starting out as a User Experience professional.
I began my career as a Business Analyst for a general management consulting firm, so my work was focused in research, process flow design/management, and learning a lot of the "soft skills" that come with consulting clients. I had a project where I was assigned the task of helping an intranet development team understand potential issues for the primary user group, document those requirements, and suggest better ways of presenting information/functionality for this persona group.
Coincidentally my brother runs his own shop for mainly front end coding work, but he introduced me to the idea of working in user experience from a business perspective (rather than technical). For the past year I've been taking on freelance work from him pertaining to mostly Information Architecture and Wireframing (as the strategy work usually doesn't come to him that often -- which is where I'd like to be someday) and have enjoyed it thus far. I'm at the point where I've been looking/applying for positions as a junior IA, junior project manager, junior UX, BA...and realize these types of positions are out there but not necessarily easy to find (you'd think they would be in NYC!). Furthermore, I realized this in consulting...that it is tough to find a company willing to take on the added expense of a junior employee that will need training and guidance.
Perhaps I am not looking for the right position titles or I do not have enough understanding of the difference between some of them - after reading a lot of these discussions I've seen some commenters make points about how different even a junior IA or a junior interaction designer may be. My hope is just to find well-structured junior level experience that exposes me to more than just doing wireframe after wireframe, but gives me a better holistic view of UX projects (how can you become a project manager without understanding other phases of a project??).
So I am looking to the community help me understand what sort of tasks/job description defines a good junior level experience and how to search for that in companies...