There are two ways that you can junk items.
Click on the icon, not the name, of an item in your inventory and drag and drop it into the junk bag. If you try to drag and drop on the name instead of the icon, it doesn't drag.
Right-click on an item in your inventory and select "Add to Junk".
These options only work if the item is unequipped.
Think of putting stuff in your junk bag as handy way of marking it as "sell this when I get back to town". When you talk to a shopkeeper, you have the option to sell everything in your junk bag.
You can view items in your junk bag by going to Inventory->Junk. You can remove items that you accidentally junked by viewing them in your junk bag, right-clicking, and selecting "Remove from Junk".
Also, when viewing items in your junk bag, you can select to destroy them, either individually by right-clicking and selecting "Destroy" or all together by selecting "Destroy All" at the bottom of the screen. You may find that you need to destroy some items if your inventory is getting because you're a greedy little thief like me who steals everything that isn't nailed down, even if you don't need it. After junking these stolen items, they may end up stuck in your junk bag because shopkeepers won't buy stolen goods. I assume there is a way to sell stolen items later in the game, but I haven't gotten that far yet.