Long post warning...

Well I meant the Monitor output (jack sockets), but the Stereo output (phono sockets) would also work just to get a signal passing through the machine. If you use the stereo outputs, then the monitor level knob has no effect. The monitor system can be connected to various other signals within the machine so will be more useful in the long run.
The 'assign' system is a connection matrix which allows you to connect sources to destinations; the sources are the 8 inputs (A-H) and the destinations are the tracks (1-24) or the stereo bus (8 connections available). The signals from the inputs won't go anywhere unless you assign them. Press the Assign button and you'll see a matrix of squares/rectangles corresponding to the signal destinations. Use a combination of cursor movements, track & stereo Select buttons and input Source buttons to toggle the source letters A-H within these blocks.
I know some people glaze over when the manual is mentioned, let alone the block diagram, but would strongly recommend you photo-copy the diagram and refer to it as you explore. It's not as complex as it looks; it's not a low-level circuit diagram but a higher-level 'logical' view of the machine. Think of it as an underground railway map - we have the London tube map here but am sure you've seen others. They don't over-complicate things by being geographically accurate; they just show how the stations are connected from a logical viewpoint so you can plan your journey.
As you work through the diagram, try and identify which parts correspond to the real knobs & faders on the top panel - quite a few are only available via the screen menus. You can see the input sections at top left - only one of the eight is shown for clarity. The signal comes in on the combo jack, its level is controlled by the Trim level control (on the top panel), and it goes from left to right via an EQ block to the Assign switch. This 'switch' doesn't exist on the top panel, but is one of the matrix assignments described above. If you assign your input(s) to the stereo bus, the signal will keep going to the right. Ignore the level control for now - this also does not exist on the top panel. Keep going and the signal will go through the Pan control and end up on the vertical lines which represent the left & right stereo bus.
Follow the lines up and you'll see the stereo bus output goes to the right, through the stereo fader (which does exist) and then to the stereo output sockets. It also also goes down to the monitor select block and then to the right, via the monitor level knob to the headphone and monitor out sockets.
So hope that helps to get you started. Once you know your inputs are getting to your PA, you can then get more advanced and assign the inputs to the tracks for recording. As mentioned in the first post, you don't have to record in order to hear the signals. If you arm the tracks by pressing the Rec button, the red lights will flash and you should be able to hear the signals from the stereo or monitor outputs. Use the diagram to see which controls alter the signal levels.
The manual shows how to set up basic recording, so you can follow the signal path from the input EQ box down into the track sections on the lower-left of the diagram. The only thing to explain here is the box marked V-TRACK. This is where the multi-track recording & playback takes place; think of it as the actual tape on an old-school tape recorder. You can also see the channel fader is to the right of the V-TRACK box (i.e. the playback side) so this hopefully clarifies another common confusion in that these faders have no effect on the
recorded level - only the source Trim controls do this.
Re. the PA inputs - the main input on a guitar amp may be too sensitive for the signal levels coming out of the dp24. If so, it may sound very distorted. Some PA's have an extra less sensitive input for playing other instruments or mp3 backing tracks which have higher signal levels. It may be a small 3.5mm jack, but depends on your PA model.
The only other tip for now is to reset the machine before exploring. A new machine will start up by loading the tutorial song. This contains several effects & routings etc. and if you create a new song, all these settings will carry over into the new song and may cause confusion. The easiest way to reset is via Menu, Preferences, scroll to the end to the Initialise item and press F4. This clears out the audio data and resets all the FX and assignments back to factory defaults. You can then save this as a dummy song called e.g. 'Reset' and protect it. In future, always load this song before creating a new one.
You
could simply use the Menu Initialise function each time, but this also resets the global preferences such as power-off options, screen brightness etc. so you'd have to keep re-instating these manually. By simply loading a dummy song, you can ensure the machine state is exactly how you want it. For example the assignment factory defaults connect inputs A-H to tracks 1-8. If you don't want this, then change as reqd. before saving the Reset 'song'. If you use a "!" character at the start of the song name, it will always remain at the top of the song list as a reminder.
Hope this has not swamped you too much! Best of luck.