How can one join the Army with an extensive criminal record?

Just based on what you have stated, the burglary is a felony, and the larceny may be too depending on the value (based on AR 601-210, not local statutes). Even if the charges were downgraded conditionally based on a deferred punishment, the Army still considers it an "other adverse disposition" and the felony(s) still stands. Add in the 2 DUI's, he is disqualified, no waiver considered. Applicants must declare all charges, and expunged charges still count. As SSG Yax said, his record will show on FBI background checks when his fingerprints are ran, regardless if expunged by local courts or was a juvenile record. The only difference with talking to another recruiter is maybe getting one that will string him along for awhile with false hope that a waiver is "possible", but he still isn't getting in.

They aren't letting in people with criminal histories anymore. They did lower that standard around 2005-2008 during the surge and need for more soldiers. The "moral" waivers. Then they got rid of that during drawdown.

I'm not a recruiter but having known friends who have done it...I don't think he's going to get a waiver for all that. This is why people need to realize that their actions in youth can and do impact their future.

There's always the French Foreign Legion if he's looking for a life change by joining a military.
- No pun intended and I am serious.
He better tell them the turth.
If they accept him, it will be because he did tell the true story - about everything.