You can try using the imagination and your mind to probe into the emotions tied to certain thoughts and experiences. Consciously experiencing a thought or experience allows the emotional baggage that is tied to it to be released.
A very common one that is helpful to release, is the fear of death. That is probably the largest fear we have, and once we take that out all other fears subside. The way to release all emotions is to face them head on and experience it out -- they don't last forever, they have an end. Use your mind to probe what it's like to be dead -- with no awareness of anything, no experience of anything. The mind is terrified to be faced with the unknown, with death, with the Void. But if you push yourself past the fear, you'll experience what's underneath it, which is peace.
Another one is fear of no control. If you want to experience that, try walking around with your eyes closed
There's a lot of just pure gut-level fear around these basic things.
Some other things:
-- this moment/state (here and now) isn't good enough for me, desire to change current experience, be somewhere other than here and now
-- attachment to pleasure / aversion to pain
-- social anxiety / embarrassment
-- desire for sex (this is probably the second biggest, after fear of death). I read somewhere that Gandhi used to sleep next to young girls, not for sex but to experience out his attachment to sex and to release it.
Another way to do all this is to work with your chakras and with kundalini. I'm not an expert on this so I can't say anything