I've been told one state in the US is the easternmost, westernmost and northernmost state. How to visit the points?

If you look at the Aleutian Islands, parts of the chain is located in the Eastern Hemisphere so technically you can consider them to be the easternmost part of the United States, but since you normally go west to get there and considering their proximity to the antimeridian it crosses Amchitka pass they could be considered the westernmost part of the US as well.

I found an interesting article about Extreme Points of the US. When people say that "Everything new is just well forgotten old" I can easily believe it. From travel.SE archives. The last airline that had scheduled service to Attu was Reeve Aleutian Airlines, which ceased operations in 2000.

I found that you can actually fly close to the Point Barrow to Barrow Airport. As far as I can tell only Alaskan Airlines fly there but I could be wrong.

The answer depends on how the question is asked. GPS coordinates (i.e., longitude and latitude) are: Pochnoi Point, Semisopochnoi Island, Alaska 51°57'42"N 179°46'23"E Amatignak Island, Alaska 51°16'7"N 179°8'55"W Thereby making the point in the U.S. that is the farthest east Pochnoi Point and the point in the U.S. that is farthest west Amatignak Island. This is fact and requires no interpretation since the longitude confirms it.

If the question is, "What is the farthest point east and what is the farthest point west in the U.S.?", then Alaska is the answer. It contains the point with the westernmost longitude and it contains the point with the easternmost longitude.

The ambiguity arises when the question asked is, "What is the easternmost state and what is the westernmost state in the U.S.?" This is because there are at least three different definitions of "easternmost" and "westernmost". (See https://en.wikipedia.org/wiki/List_of_extreme_points_of_the_United_States)

If one of the definitions of "easternmost" is used that is not the easternmost longitude, then nobody has stated what those points are. This is because if you use direction of travel, the westernmost point is in Guam and the easternmost point is in the Virgin Islands, both of which are U.S. Territories. (again, see the previous wikipedia reference).

The answer to the question needs to be given with precision. e.g., Alaska contains the westernmost longitude and the easternmost longitude in the U.S. or Guam contains the westernmost point in the U.S. by direction of travel and the Virgin Islands contain the easternmost point in the U.S. by direction of travel.