For the former, make sure you export the image from another program in a universally-compatible format or a format Photoshop can work with. (e.g., TIFF, JPEG; PSD would, of course, be optimal.)
For the latter, most Android devices come with a USB cable. (Sometimes, the USB cable does double-duty as a charger with an AC adapter.) If your device doesn't have one, you can always use a free cloud service like Dropbox. Just install the app on the Android device and log into the service on your PC via a browser. Anything you upload from the PC will show up in your Android app (to download).
There are other methods, too, like Pushbullet but that requires a software installation on your PC (if you're OCD like I am and don't like the idea of installing more software on your PC if you can help it).