I messed up along the way and I do not want to have to start over any way to fix this mistake without deleting the cylinder?
Ok to turn my comment into an actual answer:
Within Edit Mode:
Select the vertices you want to delete by pressing C and clicking LeftMouseButton on the ones you wish to delete. Use the mouse wheel to change the size of the brush(press rightmousebutton confirm selection), OR use the box-select tool, B, and drag. Afterwards press X, then V.Then you'll want to exturde the top ring of vertices using ALT+Right click, which is used to select loops. do ALT+RightMouseButton anywhere between two vertices on the top loop to select the loop(the red lines illustrate some examples of where you can ALT right click). Once selected press E to extrude. It will be automatically stuck along the local Z axis. If you don't want that press Z again. Press LeftMouseButton to confirm placement.
In Edit Mode select the vertices in question and then press the “X” key to delete them. You can also press Command + “Z” to undo your last move(s). You can control the number of times that you can “undo” in your User Preferences in the Editing Tab. If you make a change in you User Preferences be sure to save them.