Redundancy at the access layer has to parts. One is the uplink from the access layer to the distribution layer. This can be configured so that there is redundancy for each VLAN by having each access switch physically connect to multiple distribution switches (most often 2, but more can be implemented). These links in the vast majority of situations would be trunks, and as such, VLANs can be configured to be allowed on these multiple trunks thus allowing for multiple paths from the access layer to the distribution layer for each VLAN.
The other part of redundancy at the access layer, which I suspect your question was more centred around, has to do with the connection of each end device to the access switches. In most cases, each end device will be connected to an access port and thus will only have one VLAN assigned to it. The only way to have redundancy here is if the end device has multiple NICs and connects to two access ports of the same VLAN. The end device would have to have the ability to do NIC card teaming (which creates a virtual NIC that manages the two links as one) or you would have to configure some routing commands in the end device so that alternate routes, i.e. alternate NIC cards can be used if one of the two goes down. Such a configuration is usually created for servers which have high availability requirements. This is seldom done for end users because of cost (double the port usage, therefore double the number of access switches) and because that kind of redundancy is not necessary for the vast majority of end users.
I hope this has been helpful!