There are many ways to get a full time job , and it has its own benefit and disadvantage.
I personally like to work as an contractor as it means higher pay, more diverse experience and more opportunity to learn new skill.As I am single and not at a point to settle with a family , its works better to work as an contractor.Most important for me is peace of mind and zero politics.
If you want to get inside a company as a direct employee , look for contract to hire clause in your contract. This is the first step .Make sure you don't have any clauses that wont let you transfer.

Second, become essential part of the team. Somebody who can't be replaced easily in short time. One example to create a dependency is to develop your own framework or software and implement it as essential working tool.

Develop some leadership skills, you will never be hired by your client if you don't show any leadership.
Wait for right time to apply, look for openings posted on intranet. Never reveal your intentions.
Always remember if the position is higher there are inhouse people applying for it. Make sure you don't compete with your boss or you may even loose your contract job(if you are in corporate culture )
You will go through interview process but as you have gained knowledge about the culture it would be your plus point against outsiders.
Thats all..its not only one way there are many ways people get directly hired.Some don't even have to go through interviews.
What's your situation???

Thanks a bunch riverflows, working for the client for about year as a contractor for the client and as a vendor employee and have a good pay. Doing good in team. There seems to be opening that client is looking for full time employee for similar job that I do. If they hire full time, that might replace me. How is salary negotiated for full time? There is my reporting manager. There is my team lead. There are other teammates and people in different hierarchies. what would be there role for FT position?

Nothing.... After you get a green flag from hiring manager, salary negotiation is done with hr team.After you sign a contract ,You will go through onboarding process like getting badges, orientation etc .Your lead, coworkers ,reporting manager don't even come in the picture. May be they will come to congratulate you afterwards. It depends on size of employees. In my world nobody cares.

I am also in the similar boat. My lead asked me to join FT. I have been always working as a contractor. Do I submit the work experience with the client name? or Vendor Name in resume when submitting for FT?

Will have to re-do background checks. Your vendor obv wont like it and may threaten a lawsuit.

Thank you, maxpayne. Can we hear more experiences to transition from contractor to full time?

Vendor don't want their good employees to be taken away by others. You are a hen who gives golden chicken for them.
But it can worked out around the time your contract is expiring. Basically they put you in a clause not to take employment for 2 yr from your client after contract expires .But if you have a good relationship with your client as well as vendor, I have found Indian vendor won't object. It can be done through regional manager from vendor side.