When a referee does not have (neutral) assistants, how should they signal that the ball is out of play?
Normally an assistant referee would do so by pointing the flag in the direction of attack for the team who will restart play.
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This answer is based on my own experience, which is limited to lower level/youth football in Belgium.
If there is only one referee, which is common at the lower levels here, the referee blows their whistle to indicate play should stop. Then they point their arm in the direction just like an assistant referee does with a flag. In the case where the ball is obviously out of play, they might choose not to whistle.
This (indicating the direction of the throw in with his arm) is something the head referee always does in most situations. An accompanying whistle is not necessary most of the time, but in a close call situation they'll blow his whistle to indicate the ball went out of bounds (according to head referee or their assistant if they have one).
In the end, they do not do much different than when there are assistant referees.