Apparently varies by state…
In Minnesota, where I am, the return postage is pre-paid. (Yay for Minnesota!) However, you do need a witness who is also a registered Minnesota voter, or else a notary. So a college student who is away somewhere at college and knows no one else there who is also registered to vote in Minnesota, would need to go through the steps of finding a notary to witness their vote.
I think it would be highly worthwhile for absentee voters to request the ballot materials early and familiarize themselves with the specific requirements. Concerned parents could probably find out enough info online to figure out what might be particular stumbling blocks for their own child’s situation. Then, e.g., they could probably locate a notary near their child’s location (there’s very likely one on a college campus—at a student legal services office, or maybe the bursar’s office, etc., or at a nearby bank or credit union).
Parents could even request an absentee ballot for themselves, and make voting by mail be a sort of shared long-distance family activity