I know the answer is essentially "not very", but would it be a truly random assortment of weapons? How common would shields be? It seems like the shield wall was a fairly common strategy and that would require a significant chunk to actually have shields, but who's supplying them?
The organisation of the fyrd was a fairly intensively bureaucratic process, representing as it did a considerable cultural departure from the previous nature of English warfare as a rather elite affair. The logistical supply of West Saxon garrisons, for example, was codified in a document called the Burghal Hidage, which assigned a certain number of hides of land to each burh in order to supply the fyrd stationed there. The eleventh century Rectitudines singularum personarum is essentially an estate management guide, but one which establishes the obligations and duties of members of every rank of society: serving in the fyrd was a service obligation of anybody who was able to do so, which is to say any able-bodied, free man able to present himself with adequate equipment. Certain types of service could bring social status: the lithmen who effectively served as somewhere between a naval militia and a standing fleet were apparently prominent citizens of the channel port towns in whose records they appear.
The typical weapons of the fyrd were the spear and shield, both of which would have been relatively commonplace and easy to manufacture; spears were typically made of ash wood, while The Battle of Brunanburh suggests that shields were commonly constructed from lime. Owning this basic equipment would have been one of the prerequisites for service: the effective use of a shieldwall was dependent on discipline and training. The establishment of the fyrd as a quasi-standing army would have provided opportunity to actually train the annual rotation of men selected for fyrdboht. The presence of freeman individuals listed as "riding men" in Domesday and other sources, as well as the presence of clearly-trained individuals like the lithmen, suggest that properly trained and better equipped individuals may have volunteered or been chosen repeatedly for fyrd duty over the other two of the Trimoda Necessitas.
The use of armour is likely to have been less uniform. There's will evidence to suggest that some wealthy individuals left money to provide equipment in the form of mail and helmets specifically for lithmen boat crews, but the majority of fyrdmen are unlikely to have had much by way of protection beyond perhaps a helmet. Wealthier individuals - thegns ordinary, riding men and sokemen - may have had more armour, or at least a mail byrnie. There's a considerable debate as to the extent to which leather was worn as armour and the uses it had which you can read more on in /u/Hergrim's great post on the subject here, but this is likely to have been rawhide or layered tanned leather rather than the boiled leather beloved of George R.R. Martin.