How can I access Ellis Island or other Immigration Point Records?
Ellis Island records beginning 1892 are in this database https://www.familysearch.org/search/collection/1368704
Earlier New York arrivals are here https://www.familysearch.org/search/collection/1849782
You can use the Find a Collection box to look for arrivals in other locations. The keyword "passenger" will give you many to choose from.
A more versatile way to access FamilySearch's ship manifest indexes is with Steve Morse's "One-Step" webpages: https://stevemorse.org/
Another way to search the index is using the Statue of Liberty and Ellis Island Foundation's passenger search: https://heritage.statueofliberty.org/passenger
As far as I can tell, all three sites (FS, Steve Morse, Ellis Island) have the same index, modulo whatever corrections that may have been made on FS or EI, but the search interfaces and matching algorithms are very different.
Both FS and Ellis Island also have images of the ship manifests, but the ones on Ellis Island are artificially low-quality (to encourage people to purchase the better-quality image). Therefore, if you find your arrivals at EI, you should use the information from the manifest (ship name, dates and places of departure and arrival, even fellow passengers) to find the image on FS. It'll almost always be more readable.