In general, after you have selected the text, there should be a button at the top of the screen that says Copy. After you press that button, then you can go to where you want to paste, long press there, then press the Paste button that pops up.
Looks like you're using an S3 based on your tapatalk signature. Normally it shows up at the top (with cut and copy and paste icons). As B.Diddy mentions, to paste it, long press in another text box and you'll get a paste option.