Much has actually been written on this topic already. Stephen LeBarge (http://en.m.wikipedia.org/wiki/Stephen_LaBerge) being the most notable, his MILD method being one that is commonly used. Although the most common, some will find the MILD method difficult. The rewards for overcoming fears are however stark. A MILD practitioner can insert a fear to be overcome in the mnemonic used to induce the lucid dream.
I will lucid dream, I will face my fear of spiders, I will lucid dream, I am going to overcome my fear, I will lucid dream
Might be a very simple mnemonic that a person who fears spiders might use to encounter the fear within the “safe” dreamscape. This isn’t the only thing one might do, in fact overcoming a fear might not be as simple as this. Some may need many encounters with the dream fear, some may need to seek other psychological help. It’s entirely possible to become more fearful of a specific fear based on a dream encounter.
Raising the success
Regardless of lucidity method, success of overcoming fears in dreams may require several differing extra things.
1. Practice as a lucid dreamer.
First lucid dream I had, I was awake again in 5 seconds flat. It takes time to get used to the sensation. It takes effort to work out how to do thing. Especially awesome things like fly, get arms added to your dream persona, cast “spells” in dreams (the special effects limited only by your dreaming imagination).
2. Dream time ritual
We’re not noting the big old casting a circle, calling the gods of dreaming and so on. Ritual means to do things in a way that activates the mind (kinda) and a common method of going to bed with the intention to lucid dream, doing the same mnemonic every time, doing the same getting ready for bed, water, pen, slide in from the left, etc. This is a ritual that your mind takes a note of, both consciencely and unconsciously. It will help you lucid dream longer.
3. Read lucid dreaming books, and articles. (Mine are here:https://dreamsandbass.wordpress.com/tag/lucidity/ and https://dreamsandbass.wordpress.com/tag/lucid-dreams/ and https://dreamsandbass.wordpress.com/2012/10/20/the-who-why-what-were-and-how-of-lucid-dreaming/ )
4. Write in a personal journal. A personal journal helps you recap your day, write about how the fear effects your daily routine (if it does).
5. Write about the fear, what tools you could use to overcome it in the real world, and the dreamland.
Our fears can often manifest in the Jungian Shadow and be characterized in a form of malicious Trickster (see the article I wrote on these here:https://dreamsandbass.wordpress.com/tag/tricksters/ )
A trickster as a fear can be a bit harder to overcome. Many fears are based on a memory or event, taking this memory and re-dreaming it (evoking the memory then entering a dream state) then using the dream tools you have to try and combat or resolve the fear, is one method that some teach. The issue with this method is the ability to abuse it. A memory evoking, can if not done well cause continuing flashbacks. Thus this is a tool only those advanced in the art or psychologists should use.
The better method to use would be to purposely MILD into a dream with the trickster in question (give them a name) and combat or resolve them this way. Again, a psychologist might be a good consult for this method. Dream characters can fight back, making sure your in a position of power and safety in such a situation is paramount to making this a success.