How Affects Latant Semantic Indexing (LSI) to a Webpage ranking?

I am wondering about LSI. Can anyone let me know how search engine use LSI in their indexing process.

 

They don't. They can't.
Don't let anyone tell you that any search engine uses LSI.
What they DO use it simpler forms of semantic matching that recognise what the most common context for particular keywords are - what words tend to be used together, what the natural theme of a webpage should look like.

And that's how you use it in SEO - to write content that mixes in sysnonyms of your keyword and uses related terms.
Tools like Google's Wonder Wheel and the Related Search function are useful for this - they tell you what keywords Google sees as being related

 

Theme words are simply words that are commonly found to go along with key words when the keywords are used in written content found online. For example, your keyword might be “roulette”. Theme words that go with roulette might be: “table”, “bets”, “chips”, “ball”, “gambling”, and “spin the wheel”. Notice how none of these words and phrases are keywords in and of themselves, but you would commonly find these words in an article about roulette. Google looks for these! If Google does not find these, it assumes that the article or site is not as high of quality as a site that DOES include these words/phrases.

Theme phrase research finds the pertinent words or phrases that are found with the key word or key phrase you are interested in. I have provides some examples below this FAQ so you can see what I am talking about.

This will help you with your on-site SEO (search engine optimization). Using this technique will NOT guarantee you a top 10 placement for your web page. However, if you do not use this technique, you decrease your chances of getting into the top 10 by a huge amount. Not using semantic theme words puts you at a huge disadvantage to the top 10 sites that DO use semantic theme words.

Google also uses this technology in their Adsense program.

In 2003, Google bought a company called Applied Semantics, mainly to acquire the patent on their technology. Google then incorporated it into their algorithms. Do a Google search for this and see for yourself.

I have also discovered that doing this analysis on a key phrase will tell you if you niche is too broad. The defining characteristic of a phrase that is too broad is that the multiple word theme phrases that are found are commonly occurring phrases.