They need mentors (and that isn't you)
You can't be your child's best friend or mentor. You could help them find a mentor, but don't do it for them. Ask them who they would like to meet, or what industry or occupation they might be interested in. You can provide the introduction.
They need to understand how to make small talk
We all could use a little help in this area, but what does a 20-something have in common with a 40-something? Probably more than you would think. Encourage them to attend multi-generational events.
Teach them manners
If you missed this opportunity before, now is a great time to teach them how to write Thank You notes and letters. Don't assume they know, because they don't!
Encourage personal and professional development
The soft skills generally aren't taught in schools. Have them do some reading on the topic. Encourage them to be life-long learners.
Review Employment Etiquette
They will be expected to show up on time and ready to go. They need to dress appropriately. They need to understand that a college degree doesn't qualify them to be a CEO...yet.
The World of Work has Changed
When you looked for your last job, things were different. Before you go giving them job search advice, you better make sure you know the new rules.
There are some great resources out there for them and here are just a few: