How should I go about finding and hiring affordable software engineers to build my web/mobile application idea?

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.
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.

Avoid pitfalls, this article might help :-

http://khansuhel.wordpress.com/2012/06/07/increase-your-headache-by-hiring-a-mobile-app-developer-based-on-low-cost-2/

Before you start searching for developers, ask yourself a few questions. Depending on the scope of the project, you can hire an in-house professional, a freelancer, or a developer through an out staffing agency. Out staffing is when you rent a specialist from another company for a period. You can wait till your developers learn React, hire a new developer, or hire specialists from an out staffing company. Existing businesses want to automate business processes and choose between hiring an in-house or a dedicated team. As a rule of thumb, business owners want to release a new app quickly and without much investment. When outsourcing, you have work done by another company or an independent contractor. Also, most outsourcing companies offer ready-made dedicated teams with established internal communication structures. For long-term projects requiring ongoing tech support, some outsourcing companies offer post-release support services. The answer to this question depends on whether you can manage the development process yourself and the degree to which you can lead the project on your side. An app design agency, on the other hand, is supposed to provide you with project management services in addition to developers, designers, QA specialists. Another great advantage of striking a deal with a company is knowledge sharing inside the team. Good development companies document their development challenges and the ways they solve them. So over years of work, the company accumulates knowledge which evolves into ready-made components, development approaches, and best practices. Also, developers that work in an outsourcing company can ask for advice and help their colleagues. Unless you have a small task that can be handed off to a freelancer, we recommend choosing among companies.
According to research by Evans Data Corporation, the United States is the country with the largest number of developers. The United Kingdom, with 5.01% of all developers worldwide, brings in more than a third of total European revenue from mobile software development, making it the second most important tech hub in the world after the US. Germany, which has 5.68% of all developers, comes in second for revenue among European countries. According to Evans Data Corporation, by 2023, India will overtake the US by number of developers. With 79% of all Ukrainians having completed higher education and 57% of IT specialists holding STEM degrees, Ukraine boasts a great number of highly qualified local developers who are constantly expanding their expertise. At the same time, Ukrainian developers can afford lower rates compared to those in the US, Western Europe, and Australia without compromising on quality. The average cost for development services in Ukraine ranges between $25 and $50 per hour, and it is about the same for mobile app design.
Consider the things properly by asking yourself questions like:
What do clients say about them?
Testimonials from a company’s clients can tell you more than several calls with programmers.

Do they have relevant experience?
Developers may also show their portfolios upon request. Portfolios and case studies can help to define whether a company has experience creating apps for your business niche, how they approach development challenges, and what design principles they follow.

What technologies do they use?
Obviously, you should look for a company with Golang developers if the backend of your product is built with Go, for instance.

Will they steal my idea?
In terms of security, hiring an IT company is better than hiring a freelance app developer.
Besides if you do have any questions give me a call: https://clarity.fm/joy-brotonath