There are a total of 8 Letters that you need to find to spell out FORTNITE for the "Search F-O-R-T-N-I-T-E Letters" challenge in Season 4 Week 1. The letters can be picked up in any order, if you pick up an F for example, the next one you get, regardless of where it is, will be an O. You can get as many as you like in each game, but do note, that you need to either win/lose the game in order for it to count. You can't just quit.

Letter: F - Tilted Towers - On the clock tower.
Letter: O - Anarchy Acres - On the barn.
Letter: R - Risky Reels - On the screen.
Letter: T - Haunted Hills - On the stone with an eagle ontop.
Letter: N - Dusty Divot - On the pylon to the right of the crater.
Letter: I - Pleasant Park - On the wooden shelter in the middle.
Letter: T - Traingle of Trees - Next to the race track area, on the shed by the triangle of trees.
Letter: E - Moisty Mire - By the green screen, where the helicopter is.