Create a budget for the orchestra. While people will be providing their own instruments, you'll incur some expense. You must cover the cost of music stands and music, at the bare minimum. In larger churches, you may want to add in percussion instruments and special chairs for the musicians. Search online for music available to church orchestras at a good price instead of relying solely on local stores.
Line up a few instrumentalists. Ask around as you do not want to go through the process and then find out that only three people in your church play instruments. Find out if you can get a few people from each major section before you begin. Others will want to participate, but you need a base level of participation committed before you begin.
Present the idea to the decision-making person in your church. Sometimes you'll need to approach the music director while in other churches the minister may be more likely to be the person in charge. Once you convince this person to support your church orchestra, present the idea to the board for approval.
Make your case to the board. Church boards are notoriously stingy, and often with the good reason that the church budget is tight. If you want to get approval for the money, know how the orchestra can benefit the church. Have a breakdown of the first year of costs and a list of the people whose participation you have solicited. It also may be a good idea to have a couple of fundraising efforts lined up to show you're committed to the project.
Go to the congregation. Ask if anyone would like to be part of the orchestra. Explain the time commitment, which should be no more than one to two hours per week in the beginning. Give everyone plenty of advance notice about when and where the first practice will be held.
Record contact information for the people who express interest. Call them as a reminder a day or two before the planned first practice session. You want to hit the ground running, and you need everyone there to make the day a success.