Generally, non-essential personnel get sent home without pay.
However, when the dust ultimately clears and a budget is passed, they get the back-pay, to be made whole.
I have a friend who recently retired from civilian service for the Navy (JSF program engineer). He's gone thru this twice in his career IIRC. He has said it's like getting a week or two unplanned, delayed-pay vacation. Admittedly, money was not tight for he and his wife, so they could endure the temporary loss of pay. Others may not be so fortunate in the short term. But in the long term, it's not a big deal according to him.
The other question is what effect it has on citizens waiting for civil services. Some things will be exempt and continue to function. Other things will grind immediately to a stop and then pick back up when the budget passes. So there will be federal services that get interrupted and cause issues for us common folk.