The Setup

Get a couple of probes from the equipment pouch, and connect them to the 1 and 2 inputs of the scope.
Use colored rings to mark the probes

Capturing one waveform

Turn on the scope (bottom left button on face).
Turn on the board (make sure the battery is fully engaged in its connector.
Connect Probe 1 to TP 1, and ground it, i.e. connect the alligator clip to the GND connector on the board.
Press AUTOSET (black button, middle right of face)
You should get your first waveform, which is referred to as a square wave.

Move the waveform up and down using the two buttons around the yellow 1 button
Move the waveform left and right using the large pan button (top middle of the face).
Scale the waveform and magnify or reduce it with the smaller zoom button, around the pan button.

The scope has two horizontal cursors you can move around, as well as two vertical cursors that allow you to measure time differences (horizontally) and voltages (vertically).
The cursors are turned On/Off by the small Cursors button (top left of the face).

Move the 2 vertical cursors to measure a full period of the signal. Report the time you measure.
Click on Measure (center top), which will bring in a menu at the bottom of the screen.
Click on Configure Cursors and set the cursor mode to display Hz instead of seconds. Click on Configure Cursors one more time to remove the menus from the screen.

Click on Cursors another time to control both horizontal and vertical cursors
Use the Select button to switch between horizontal and vertical cursors
Use the Multipurpose a and Multipurpose b buttons to move the cursors.

Question: Why, do you think, isn't it 5 Volts, since the power supply of TTL circuits (e.g. 74LS00) is 5 Volts?

Connect Probe 2 to Test Point 3
Autoset
Press on 2 to bring Waveform 2 on the screen.
Notice that Waveform 1 (yellow) appears very clearly, but Waveform 2 does not.
This is because Waveform 1 is faster than Waveform 2, and the scope by default synchronizes itself to the signal on Probe 1.
To get a better picture of what is going on, we need to take snapshots of the waveforms with the single button, while playing with the Scale button.
Go ahead, change the scale a bit and press Single. Repeat a few times until you feel you have captured the repeating nature of both waveforms.