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.
http://www.youtube.com/watch?v=JPHSG_lLKJ8

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.