To sell an item in your Home Garden, select the item you'd like to sell and tap the "Sell" button. You will always have to confirm your action either by tapping the Sell button twice or by confirming the sale in the separate pop-up for more valuable items.
If your Coin Storage is full (yellow colour fills the coin bar completely), you will be given an option to delete the selected item instead. You can either spend some Coins on something or you can add more storage by tapping on the store icon at the bottom left of the screen and looking in the tab with the hammer icon. Purchase and merge some Coin Caches to increase your Coin Storage limit.
The second issue may be - if you can't sell items - that you've lost the info bar at the bottom of the game.
Just tap on the small arrow to show it again:
If you're still having trouble and this FAQ doesn't help then please get in touch at MergeGardens@FutureplayGames.com