Compile a contact list of local shops and organizations that may be interested in distributing your magazine. Think about what you've written and who it may appeal to, and then discuss your list with a colleague. This will give you a different perspective and possibly bring up other places to distribute the magazine that would not have previously occurred to you.
Divide the list in half between yourself and your colleague. Write a script explaining what the magazine is, what you do and why it might be a good fit for the place you're contacting. Practice your lines until you get comfortable, then make the first phone call or visit. Ask to speak to the manager, explain who you are, and ask if they'd be willing to stock the magazine.
Be prepared for not getting an answer immediately. Many people will want to check with a supervisor or see a copy of the magazine first. If this happens, arrange to drop a copy off or mail one out. Arrange a time and place to get back to them about it. Be courteous and thank them for their time. Make a list of everyone you have to call back and mark on a calendar when you have to do it.
Deliver your magazines. If you can, deliver by hand. This will add a personal touch, and help build a relationship between you and the people who carry your magazine. Modify your script to be more general and use it to contact the local press. Explain that the magazine features local talent and ask if they'd be interested in covering it. If they are, arrange a time to come in for an interview or discuss it by email.