Members in the delivery community should be able to help find a site and sometimes will offer a garage, porch, or yard. If that is not feasible, churches and community centers are often receptive to housing a weekly distribution. Look for a good-sized room, garage, courtyard, or other area that is accessible to a truck, can get a little muddy, and can be used for about five hours each week. Indoor or covered space is nice but not necessary, as vegetables don't mind getting wet. If your distribution is on-farm, you may wish to designate an area of the barn or of another outbuilding that is safe for children and won't create a nuisance for you.
Some growers deliver their produce in already bagged or boxed shares.
Prepackaging is a lot of work for you, though, and so unless you've got a particular reason for doing it, setting produce out in bulk may be easier. A bulk distribution usually involves a chalkboard with a list written out every week, telling members how much of each vegetable to take. With a bulk distribution, you will almost certainly need a site manager. Most likely, whether the distribution is on your land or not, you'll have time to drop off the goods, but won't be able to stick around for three or four hours to make sure every family gets its share. A site manager is a non-farmer who fills this role.