If I live in Arizona and am getting a divorce. I have been told that I must give my spouse 1/2 of my 401 K, is this true and is there a penalty? How is the money distributed? A check directly to him? We are not using a lawyer we are filing the papers ourselves?

There is not one rule fits all. You can give him 1/2 if you and he agree that is fair.
Things on how long you were married, earnings by each during marriage and many other issues can be looked at. But of course that is where layers and argument come in.

Personally, it would be worth it, for both of you to at least hire one lawyer together, and share the cost to go over all the details. And make sure it is all in writing.

Arizona is one of the 9 community property states, but that doesn't mean that you have to literally cash in half your 401K with penalty.
List property/assets on paper and then pay a mediation lawyer together, just for advice. Do them in chronological order. Assets from before marriage aren't community property.
Or figure it out yourselves, if you don't have children and are on good terms.

It is quite common to split retirement assets such as an IRA or a 401(k) 50:50, particularly if you have been married for ten or more years. However, you must strictly follow the correct procedures, which allows the split to happen like a rollover, penalty and tax-free. Otherwise the IRS will treat the split as a distribution and will require payment of taxes and penalty. The key is to have a a Qualified Domestic Relations Order (QRDO) issued by the court. Here is an article that explains it pretty well: Divorcing? The Right Way to Split Retirement Plans