Did you check if your SD card is formatted ok?
If you don't have any data on it yet, you could try reformat it with phones internal formatter.
Sometimes the SD card misbehaves when not "correctly" formatted.
Do use some known brands for your SD card (SanDisk - best choice, G.Skill - I use this one, Sony, Kingston, etc.)
Take note on SD card capacity too, 32GB max capacity is officially supported, but anything bigger is matter of luck.
About data transfer, HomeBoy suggested File commander application for data transfer, I personally use ES File Explorer and think it is great application with a lot of features, but both are usable for data transfers.
When not using any file explorer apps, you can only use internal "move to SD card" option for pictures, music and videos, as alexdon already said in his post.
In the end, some thing can be change at the very beginnig, eg. when using camera, you can change settings where pictures are going to be saved.
Do (re)check some of this suggestions, maybe you'll find solution for your problem.
