There are many ways to get in and it can get very confusing.
Place yourself in the top 8 of the US open, or win one of the four 'Major' titles, ie: British Open, The PGA championship. Or finish in the top four and you will get an invite for the next year. If you win the Players Championship (Sawgrass) you will be invited for the next three years.
Finish in the top 30 of the Official PGA Tour cash List for the year. Then your Masters invite for the next year is guaranteed
Finish in the top 50 players of the Final Official World Golf Ranking (Taken from the week before The Masters starts)
Win any PGA Tour event since the last Masters tournament, that awards full FedEx Cup points toward the Tour Championship
The Masters Committee has the discretion to invite any international players who don't otherwise qualify. ( they say they're trying to get the best field of players)
Win The Masters and get a lifetime invitation (any top 15 player is invited back next year)
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It depends which tournaments you are talking about. If you mean professional events such as PGA Tour etc you will need to be a tour member, Monday qualify or get a sponsors invite. If you mean like Amateur events, there will usually be a website from where you can get an application form, you send it in and see if you make the cut to play the event.
ANSWER:
Any professional golfer, or any amateur with a USGA men's handicap index of 1.4 or lower, can attempt to qualify for the U.S. Open golf tournament and just fil in the required requirements and submit an application form