This is a very broad question. What do you mean by compare two paragraphs?
You could actually "compare" two paragraphs using a string edit distance function without doing any parsing. See: https://en.wikipedia.org/wiki/Edit_distance
Going one step further, I used a shallow approach where I only considered POS tags and words, you can read more in my MS thesis here, starting page 19: http://josep.valls.name/wordpress/wp-content/uploads/2011/09/MCVAI-JosepVallsVargas-0905.pdf
If you want to use the full syntactic or dependency parse, you will need to dive into the world graph similarity. Read more here: https://en.wikipedia.org/wiki/Graph_theory
Finally, one of the latest trends in the pharaphrase identification community is to use word2vec which is a tool released by Google to compute word embeddings. You may want to read through the responses of this SO question: How to calculate the sentence similarity using word2vec model of gensim with python