They are not, by the way, related to common garden gooseberries. We just bought an older home whose evergreen shrubbery looks less than respectable. The arborvitae have a lot of dead branches and the backs of the junipers are almost entirely bare. But, if you're determined to try to keep the old bushes, start by removing all dead wood during late winter or early spring when the plants are dormant. At the same time, cut each long, live branch back to a junction, retaining some green foliage and being careful not to leave stubs.
Judgment is required here.
Cut back too hard and the plant may die. Leave branches too long and you're left with a scraggly specimen.