What is the normal entry-level rating for a Master? IM? GM? 

I understand that these titles are earned at tournaments, but is there a point threshold at which the title is automatically awarded? (2000?) If not, what is the average Master rating?

IMs I believe are 2400+, GMs are 2500+. I believe world-class GMs are generally ranked around 2700 or more.

Wikipedia sez:

The United States Chess Federation (USCF) awards the Title of National Master to anyone who achieves a USCF rating of 2200, and the title of Senior Master to anyone who achieves a USCF rating of 2400. The USCF also awards the Life Master title to anyone who holds a 2200 rating for a total of 300 or more games in his or her lifetime.

FIDE Master (FM) is a title awarded by the world chess governing body, Fédération Internationale des Échecs (FIDE). Introduced in 1978, FM ranks below the titles of International Master and International Grandmaster, but ahead of Candidate Master. The most usual way for a player to qualify for the FIDE Master title is by achieving a FIDE Rating of 2300 or more.

The title International Master is awarded to outstanding chess players by the world chess organization FIDE. The title is open to both men and women. Instituted in 1950, it is a lifetime title, usually abbreviated as IM in chess literature. FIDE also awards the lower title of FIDE master (FM) and the higher title of Grandmaster (GM).

Normally three favorable results (norms) in international tournaments involving other IMs and Grandmasters are required before FIDE will confer the title on a player. IMs usually have an ELO rating between 2400 and 2500. Sometimes though, there may be a very strong IM who has not yet become a Grandmaster, over the rating of 2500.