I am new to the Show Business, but am not new to magic. I have a good thirty minute show put together. I have partner. We have never put on a show yet, but want to get one at our local library. How do I go about tis. I tried a few months ago, but the never got back to me after I tried to get back in touch with me. They did seem very Interested too though. Also, if it matters, the library would probably pay us.

Here is a list of our tricks (in order of performance) :
1) Vanishing Coke bottle (together)
2) Food to go
3) Rubicks Cube
4) Spirit lights with change bag (together)
5) Whats Next (Hopping spots)
6) Vanishing Deck
7) I give invisible cards to a kid and they shuffle them and I do spongeballs while they are shuffling (for some humor)
I then do the invisible deck
9)Strat o Sphere (together as a short skit)
10)Fiber Optics
11)Rising card
12) News flash

if that show last's only 30 minutes you're dead. a 30 minute show contains 4 to maybe 5 effects. with 12 effects I don't see any time for patter and audience inter-reaction.

I agree with Paddy about the show. I don't know how much experience you have with kids shows, but you should test it out before doing a library show. I've only done one library show before (I'm 17), but there was a lot of families there, so it is like a showcase of your talent. You don't want to have a bad show there (you never want to have a bad show, but especially not when there are many people).

For the business side of the show: when I was maybe 15, I emailed a library asking if I could perform a show for them, but it didn't work out. Then about a year later, another local library called me up and asked if I could perform a show for them. It was a paid gig and everything.
I would advise you to call libraries asking if they would like you to perform for them. You can determine whether or not you will charge money. Since you are new, a free show would also do wonders as advertising (presuming that you're a good magician). But, as I believe Paddy says, free shows lead to more free shows. So if you do do it for free, make sure not to tell everyone or else they will expect a free show, too. Don't lie and say that you were paid, but phrase it that "this library hired me" as it somewhat assumes that you were paid, but not always.
The main reason I didn't get the first library gig was because I was an inexperienced magician and business man, so I only wanted to perform about 15 minutes of magic so that they wouldn't have seen my whole show and have no reason to hire me. It wasn't worth it to only hire me for 15 minutes. Now I know that if you perform your entire show, people will hire you because they want to see the whole thing again, but at their event. You look like you plan to do an entire show, which is good, but just make sure it works well with kids and research kids' magic shows. I don't think that an invisible deck would play well to kids. Both cards and mentalism can get messy with kids, so putting them together could make it very sticky.
If you make your show about reading, you will definitely get booked (pun intended). Just change around some tricks' purpose so that they are about the wonders and joys of reading.

So first: create a solid kids show and test it on real kids
Then: Contact the library, make yourself and the show desirable, and then get hired

I highly recommend feasting your eyes on some Silly Billy performances.

As someone that does lots of Library shows during the summer I must say you are going about it all wrong. Libraries should be paying you but you should also be doing a good show that benefits the library. The reason why libraries have performers is to bring people in to the library and have them check out books. If you want flight time I would say go to a low end daycare and offer the show there. Major cities and town libraries have a budget and deserve top notch entertainment.