Like how would they fasten them to their backs to be able to grab it when needed. Like a swords sheath
Outside of combat, ancient warriors would not be ready to fight. They generally wouldn't be wearing their armour and their weapons would be stowed away to protect them from moisture and wear.
Militias like the armies of the Greek states formed large throngs on the march, with most of the weapons and other heavy equipment loaded onto wagons or carried by enslaved people. The Greeks took it for granted that every hoplite would bring at least one attendant (usually an enslaved person, but sometimes a younger relative) with him on campaign, to carry his gear, build his shelter, cook his food and so on. In camp, these attendants might keep their gear with them, or, in the case of the Spartans, they might be forced to pile it up together in the centre of the camp to discourage them from grabbing the weapons for themselves and revolt. Only those on guard duty would actually have their weapons on hand. On the march, if battle seemed imminent, the attendants were expected to quickly hand over the shields they carried and then keep themselves on hand to carry away the wounded if necessary.
Professional armies that cared about reducing the size of the baggage train might forbid the use of these attendants, or reduce their number. The result was a leaner, more flexible marching force - but one that had to carry its own equipment. In these armies, shields might still be piled up on wagons, but they could also be carried on individual soldiers' backs in a protective bag or sheet. Roman legionaries, for instance, carried their large shields on their backs in protective leather bags fastened by a leather strap below all their other gear. If there was a sudden need to fight, they would need to set down their weapons and tools, drop all the other equipment, take the shield out of its bag, and then pick up their weapons again.