I hope this answer will help you in two ways: It should help avoid unnecessary expense being incurred and it should also help you recruit software engineers to build your project.
Before you spend a single dime on building, I'd encourage you to validate the idea itself with potential customers. Identify the kind of person you are thinking of solving a problem for, and just explain the high-level concept. Make sure that a sufficient percentage of them are saying "yes, I need this." Then, really distill the idea further into a single piece of functionality that this customer base says they want.
There are tools that allow for "drag & drop prototyping" like fluid.io that you can use to create a clickable walkthrough of the user flow you're looking to create. The more that you can do to validate the idea and focus it, the more you can define your "Minimum Viable Product."
If you can't find enough of your potential customers to get excited about the idea, I would advise against hiring anyone to implement anything.
That said, it's also a lot easier to recruit talent when you can say "I spoke to 100 potential customers and 40 of them said they would use this" or better yet, pay for it.
Convincing anyone to work on your idea will be considerably easier if you can show some existing proof or interest around the idea.
From there, your best source (assuming you don't have a network of people to draw from) might be local colleges & universities. I would advise against hiring online or working virtually with someone when you are new to building product.
I'd be happy to talk to you about your project, how to validate the concept and how - if you decide to pursue it - to hire good talent.
Best of luck!
I have encountered similar challenges when both hiring for a company on a tight budget as well as when implementing my own product ideas. There are a few paths you can take here depending on what you are trying to create.
For well-known domains with tight specs, you can go with fairly inexpensive contractors offering their services via elance.com or odesk.com.
If you have a high level vision of your mobile app but still need to identify product market fit, you have a couple options:
1. Build it yourself even if you don't have a technical background. The barrier for entry on mobile prototyping has been lowered thanks to WYSIWYG editors such as Appery.io which will work across Android, iOS and Windows Phone platforms.
2. Participate in a Hackathon. Folks at most of these events are young, friendly and looking to network. So if you have a compelling idea and can offer value towards the project (i.e. design, art, etc), you will find many like-minded folks who are willing to pair up with you. If you are not located in a tech centric city, you can always join virtual hackathon events via Hacker League https://www.hackerleague.org/.
If you have additional questions, ping me via clarity and I am happy to discuss further.
From my experience I always start with my local network connections. I then would look for "app developer meetups" in my area for networking opportunities.
You can choose portals like Elance, Odesk etc. to find the best developer for your app
An other resource you could test the water in is http://www.theymakeapps.com . They have a pretty extensive listing of app developers, along with information on what platforms they build on, and how much an app usually costs.
Your question "finding and hiring affordable software engineers" would make me ponder your current business plan - idea ... I would ask myself first... how is this app going to fund itself over time?
You mentioned affordable software engineers which begs the question have you worked up a start-up / launch budget?
Most apps take about 100+ hours to get to version 1 beta ... plug in the current development rates from your research to help with your budget numbers
Here is a great video that takes you behind the scenes of the making of the Airbnb iPhone App...its a great snap shot of app creation.
There are many "affordable" but extremely busy engaged developers available...I suggest that you understand your numbers first before engaging with a company.
Hope that helps you get going in the right direction.