I use Linux for my PC operating system. That means I don't get any fancy Android File Transfer programs to use to copy files on and off of my devices, and setting up MTP support is a hassle -- not to mention the closed nature of the whole mess. I can use the command line and adb to copy files back and forth, and sometimes I do, but the easy way is to use an app that acts as a remote server and "browse" my files with Chromium or Firefox. They also work with Windows or Mac OS for those times when you don't want to look for a cable.
There are plenty of apps available that will work. Airdroid is a pretty popular one that also offers the ability to send and receive SMS message through your PC. It's also free, and free is always good. I like things a bit more lightweight and simple, so I use Wifi File Explorer Pro. It's not free ($0.99) and doesn't let you text from your PC. It's just the first one that was made available and I hate change. My point is, there's plenty of apps that will work, and they all work basically the same.
- Grab the app from Google Play, install it, and run it.
- The app will tell you a URL to put in your browser. You may need a code or need to scan a barcode to log in.
- When the page loads, you see everything that's on your phone storage, and can transfer files both ways, or play music or video.
The apps are actually running a tiny web server on your phone, so the result acts like a website. You will need to have both machines on the same Wifi, and in theory a cable is faster, but wireless file transfer is pretty darn easy.