Having gone through this multiple times either in new startups or for side projects, here is how I would approach turning your idea into an app.
1. Defining the Minimum Viable Product
Your first goal with any new idea should be about proving the idea and finding a market that wants the app you want to build. Achieving that quickly is probably one of the most important thing.
To achieve that, you will need to write the specifications that will constitute your MVP. The MVP is basically the simplest expression of your idea to prove it.
This step should not cost you much as you can do this on your own.
2. Design the app
Before starting any development work, I would suggest you work with a good UX/UI designer to create wireframes and mockups of the app based on the specifications you came up with in step 1.
You can find good designers in meetups & hackathons or on website like Dribbble or 99designs.
If you want to reduce your costs, you can give shares in the project to the designer. Otherwise, it really depend on the size of the MVP but I would say it will probably cost between $5K-$10K.
3. Develop the app
Once you have the specifications and the design of the app, you now need to find a good developer that will build it.
Again, you can find good developers in meetups & hackathons or on sites like Github.
If you want to reduce your costs, you can give shares in the project to the developer. Otherwise, it really depend on the size of the MVP but I would say it will probably cost between $10K-$25K.
For this part however, I would recommend the developer becomes part of the project as his engagement will most likely be higher.
4. Test the app
This step is not only about making sure the app is bug free, it's also making sure the app does what was intended in the specifications.
To test the app, you can use platforms like BrowserStack or SauceLabs which gives you access to multiple devices/browsers.
You can do this step on your own so the cost will be for the subscription to the test platform which would be around $100/month.
Hope this helps and good luck with your project.