There is plenty of useful information online, eg. https://bible.org/article/starting-church-library but it is mostly aimed at larger church libraries in the United States.
This advice is for church libraries with up to about 2,000 books, especially New Zealand or non-US church libraries. These are just some thoughts and suggestions from my own experience as a church librarian. My training is as a lawyer and educator rather than a librarian, so I have benefitted from lots of advice from others, and wish to share what I have learned.
You need a regular budget for replacing stale books, replacing missing books, and getting new books. If your budget is small, you can find Christian books in op shops, fairs, and second-hand shops, as well as great specials in the Christian bookshops. Donated books can be helpful, but be selective - what you leave out is as important as what you put in. No-one will use your library if it is dominated by dusty old books from a by-gone era.
For advice on selection, see "Selecting books" in the menu, which includes information about Christian book awards around the world.
Second-hand book shops in New Zealand:
Books need protection. Large rolls of coverseal (suitable for paperbacks) and other library supplies can be purchased from http://bookcover.co.nz
Avoid direct sunlight - it makes books look old really fast.
The library needs to be visible, accessible and inviting. Make sure at least some of the shelving is where people regularly go, such as the church entrance. If you can't position your entire collection in a prominent area then consider putting a selection on display in a prime position.
Shelves should be at eye-level as much as possible - you can get tilted display shelves for the bottom level. Use book stands to display some books with covers showing rather than just rows and rows of spines!
In my view, small to medium-sized libraries are better to use a limited set of categories rather than the Dewey Decimal system. The books can be colour-coded into categories using coloured dots available from http://bookcover.co.nz/. Within each category, the books can be shelved by the first letter of the author's surname, written on the coloured dot.
Feel free to copy or adapt the list of categories in the menu to the left.
Books should be displayed in an eye-catching way, and the display updated frequently. You can showcase recommended reading, new books, or books on a particular topic.
People are most likely to read books that are personally recommended. One idea is to ask some well-known people in your church to choose one book each that they've enjoyed, and to give you a few words of recommendation (e.g. "Entertaining and insightful" or "Helped me through a tough time"). You can then create a display of these books with "recommended by" cards.
You might like to include a "book of the week" in the order of service, using the blurb from the back cover or cut and pasted from amazon.com.