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.
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 his whistle to indicate play should stop. Then he points his arm in the direction just like an assistant referee does with a flag. In the case where the ball is obviously out of play, he 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 he'll blow his whistle to indicate the ball went out of bounds (according to him or his assistant if he has one).
In the end, he does not do much different then when he has them.
If you'll watch some full game videos, on youtube for instance, you'll see him do it.