Check out Dan Poynter's website for lots of free information on publishing: http://www.parapublishing.com. Write it the best that you can. Have several people read it over and offer editing tips. Design a cover and maybe some interior graphics. Submit your manuscript to a print-on-demand publisher such as www.createspace.com.
Report Bob's answer
Before you begin, you might want to think about a few things:
1. Who is your target demographic -whether you just want to pass it out to friends and family, or try to get Barnes & Nobles to sell it will determine the paper quality/whether 2-color or 4-color/saddle vs. perfect binding,etc. This then determines how much it will cost which in turn determines how much (and what kind) of advertising you want in it...if any.
2. Is it for fun or to make money. If not-for-profit, consider what a reasonable amount is to spend and work backwards from there. If for profit, you should spend a good amount of time thinking about how you're going to make money off of it, and then test those avenues to see if it'll actually derive income. Most for-profit publishing endeavors that fail, do so because they didn't spend enough time thinking about exactly how it was going to make money for them.
If you've already thought through those and are ready for publishing, you can go through an online publisher or storefront. Alphagraphics based out of Kansas City is a good place to start for storefront. As with any storefront, you're going to want to call and speak with the owner first and see what kind of discounts you can get. They will be even more likely to give you deep discounts if you let them know it is not-for-profit (if that's the case). For internet publishers, you have to find a place that has both a good quality and good prices. Google "Dazzle Printing"...they are an online based print-on-demand publisher that is both high quality, low cost, very professional and relatively speedy.
If cost is an issue, you might want to approach a media/design professor at a community college, small college or art institute, to see if they will let their classes know about your project. The benefit for them is that they can begin building a portfolio and make a little change (everyone needs money in college), while you get your magazine layout, formatting, and possibly photography done at a high level for a low cost. If you need someone to read/edit it for you when you're done, you can always email me and I'll take a look at it.
Hope this helps.