The assembly wears no liturgical vesture. There is no universal rule governing this choice. It may be bound at the waist with a cincture. Altar servers frequently wear an alb or its shorter version, the waist-length surplice, donned over a cassock. The vestments for all ministers other than priest and deacon may be determined regionally.
Servers wear vestments by local tradition more than by church law.
A customary vesture of readers or communion ministers is less generally observed. Within a particular parish or diocese you may see communion ministers in an alb or some other local vesture. Some communities ask their ministers to wear a pin or pendant identifying their service. Liturgical attire for communion ministers may lend to the solemnity of the ceremony, but dressing like others in the assembly may emphasize the service all are called to render. Thoughtful readers and ministers of communion who wear no liturgical vestment generally want to appear appropriately dressed for their service.