Adding a Deal
There are a couple ways to add a deal to the pipeline, which will always add it to the first stage. Look for the ribbon icon : 
On both the History and Search Deals page
By clicking on the ribbon on the far right of each deal row
When clicking on the deal row first, the modal also ha the ribbon on the bottom left that you can click
If you open the deal in a new tab, there is a "Save" button where you can add it
Removing a Deal
Similarly to where you can add deals to the pipeline, if the ribbon has a "check" mark in it, it means it is in the pipeline. Clicking on that ribbon again will remove it from the pipeline. This can be done in all the same locations as mentioned above. In addition, when you click on the deal while in the pipeline, the familiar modal that opens allows you to remove the deal from the pipeline as well.
Stage Management
All users have the ability to add and remove a deal to pipeline, as well as drag/drop the deal through the preset stages. If you are an Ultimate user though, you can also
Add custom stages
Rename stages
Delete individual stages. NOTE: this requires you to move all deals out of that stage before you can delete it