The Copy-Paste Gadget will allow you to copy an area and place it somewhere else, without destroying the original. You can also place structures other people have made online!

Right click on one corner of the area you want to copy. This block is where it will be placed from later on. Sneak right click on the other corner to copy the rectangular area between them.

Hold G then change to Paste mode, and you will see a hologram of the blocks you copied. You can anchor it somewhere and then hold sneak and right click to adjust the structure's location manually, if it's off at all. 

You can save structures to Templates.  Templates allow you to save copied structures into items, so you can save them to paste them more later.  

If you don't want to have to get all the blocks for your structure, you can use Construction Paste instead!

The Template Manager is where you manage Templates, as the name implies. 

 

Place the Gadget in the left slot and Paper or a Template in the right slot.
Click Save to write the structure data in the Gadget to the Paper, creating a Template. You an also overwrite Templates instead of using Paper.
Click Load to write the structure data in the Template to the Gadget, allowing you to paste it into the world.

Click Copy to copy the structure data in the Gadget to your computer's clipboard. You can post this online or send it to someone out of the game and they can load it.

Click Paste to paste the structure data from your computer's clipboard to the Paper or Template in the right slot, so you can load it into the Gadget.

You can also find user-made structures online here!

Explore that page and find a structure you like and open the post it's in. The post should have a link to pastebin.com, and at the bottom should be a text box that says "RAW Paste Data." Select everything in the box and copy it.