In general, Ugaritic studies help us:
1. To understand the Hebrew language (lexicon and syntax, especially). Many Hebrew "homonyms" were eventually revealed to be orthographically identical, but actually derived from different roots, the sounds of which were represented by the same Hebrew letter.
2. Religious texts give us the mythological background to Canaanite beliefs and practices.
3. Literary use of words, especially symbols and poetic usages, are often clarified or amplified by the Ugaritic texts. This is especially true of the Psalms, although one has to be careful of pushing parallels with Ugaritic too far. This is a matter of continuing debate.
The classic works on Ugaritic parallels to the Hebrew Bible are by L.R. Fisher:http://iac.cgu.edu/uhpp.html
I've used his works a lot. Also Dahood's Anchor Bible commentary on the Psalms is considered a classic, although he's been criticized for trying to treat the Psalms as if they were themselves Ugaritic texts and not Hebrew. But you'll find a lot of proposals for interpreting the Psalms from a Ugaritic perspective.
These are enough to get you started. If you're interesting in further study, there's a ton of resources. Just look at the Wikipedia article for Ugaritic or google "ugaritic bibliography". If you want to go really hardcore, PM me and I'll point you to the standard works and bibliographies.
Hope this is helpful.