Before you run to a computer and try to hack what limited things can be, make sure when you're creating a New Save that you select the Detective class, as you'll start your game with the necessary "HACKMAN 1" to actually begin hacking in the first place.

When you load into the game run over to your office's computer and you'll be greeted by the extremely disorienting Hacking UI. At first it may seem incomprehensible but once broken down, is very simple to understand:

The strange interconnected web of names is just a visual representation of the Device Network, showing every device that can be hacked within your current loaded area. So for example, when looking at your office computer, you'll see device names such as "Intranet" (your hacking device) and "5Security Camera" (a security camera for a room somewhere in the building).

To choose what device you want to connect to, you use the empty IP Address box. Each network device starts with a specific number that when entered into the IP box, changes the loaded screen to be that of the selected device (for example, typing "5" would bring up the security camera screen locked behind a firewall).

Then to start the actual hacking side of figuring out passwords, we turn to the CHAR, HEX, and VISUALISE. The CHAR heading will show a variety of typable characters, the HEX showing the character's equivalents in the games own hex-code, and the VISUALISE being pretty much pointless.

The final pieces of the UI are then the small + and - buttons, each one cycling forwards and backwards respectively through the different combinations of characters/hex-codes.

Now that you (hopefully) understand what the hacking interface means, you can finally learn how to do some hacking.

First, enter the number in the device name of whatever device you want to hack into the IP box, for this example I will enter the "5" from the "5Security Camera".
Next, select the CHAR button to make characters appear rather than their hex-code equivalents.
Now filter through the different combinations of characters using the + and - buttons, following the trend of there being more alphabetical characters rather than symbols, until you eventually find a complete word to be used as the password such as "SOVEREIGN".

And there you go! You can now go and abuse your hacking skills to whatever extent you wish.

Thought I'd throw together a few things I've discovered whilst messing about with the hacking device here just to see if anyone could expand upon them:

After successfully hacking any of the vending machines, you're able to set the prices to whatever you want giving an easy way of getting some free healing items early on.

Going back to the aforementioned relation between the "HEX" and "CHAR" displays, I've compiled some of the equivalents between the hex-codes and the characters below:

30 - 0
31 - 1
32 - 2
33 - 3
34 - 4
35 - 5
36 - 6
37 - 7
38 - 8
39 - 9

41 - A
42 - B
43 - C
44 - D
45 - E
46 - F
47 - G
48 - H
49 - I
4a - J
4b - K
4c - L
4d - M
4e - N
4f - O
50 - P
51 - Q
52 - R
53 - S
54 - T
55 - U
56 - V
57 - W
58 - X
59 - Y
5a - Z

61 - a
62 - b
63 - c
64 - d
65 - e
66 - f
67 - g
68 - h
69 - i
6a - j
6b - k
6c - l
6d - m
6e - n
6f - o
70 - p
71 - q
72 - r
73 - s
74 - t
75 - u
76 - v
77 - w
78 - x
79 - y
7a - z

Any hex-code from 80 - 9f is "filler" (has no character equivalent but shows no gap when viewing CHAR, just an added layer of confusion).