Android - How do you merge decks in Anki?

1. Open AnkiDesktop.
2. Open the "Browser".
3. Click on the deck you wish to remove on the left-hand pane.
4. Hit ctrl+a (command+a on mac) to select all cards.
5. Click "Change Deck" at the top.
6. Select the deck you want to keep in the pop-up dialog.
7. Click "Move Cards".
8. Repeat steps 3 - 7 for all decks you wish to merge.
9. Go back to the "Decks" screen in AnkiDesktop.
10. Find the empty decks (the decks you wish to remove will have a card count of null).
11. Delete those decks.

Using AnkiDroid, you can move a note to another deck. So you could do it for each card, then remove the empty deck.

But that would be a pain if you have many cards. In that case, I recommend using Anki Desktop too:

1. Sync on AnkiDroid
2. Find a computer and install Anki Desktop on it
3. Sync on Anki Desktop
4. Move notes like you need, you can select many cards and move them altogether
5. Sync on Anki Desktop
6. Sync on AnkiDroid

Disclaimer: AnkiDroid developer

Because this answer from 2014 still comes up top in a google search in 2019, I thought I would add to this that, at least on a Mac, the latter part of the above answer is out of date. On the version of Anki I am using, the first part of the instruction stands: i.e. click 'browse', choose the deck you want to move cards from, click on one of the cards in that deck, and then use command+A to select all. This is then when the instructions depart from the old ... now click 'cards' on the top left of your browser, and then select the first option 'change deck'. A pop-up will then appear, and within this select the deck you would like to move the cards to, and press the blue 'move cards' button.