Easy hacking
If you move your cursor throughout the symbols, sometimes you will highlight a group of symbols. Selecting these "duds" will remove one of the words that is wrong from your choices. Also, it may grant you an additional attempt if you have already gotten a selection wrong.
Only use three attempts during a hack, so you leave yourself with one to back out. Then, go back to the attempts screen, and you will have four more chances. Repeat this as many times as desired.
Search around both fields, and you will find a string of symbols that you can enter as the password. It starts with "(", "<", "[", or "{" and ends with the same symbol. This will completely refill your password attempts.
To hack "Very Easy" and "Easy" computers (and "Average" if your skill level is high enough), look for the secret characters first. If you find enough of them, there will often be fewer than four passwords remaining after the duds are removed.
To hack "Average", "Hard", and "Very Hard" computers, use the following steps. Look for common suffixes, such as "-ing" or "-ed". You can even go one step further by adding repeated letters that precede them, as in "-ted", "-ded", "-ling", "-ring", etc. Write down or remember the entire list of words in suffix groups. Choose a word from one of the suffix groups, preferably the largest one, and look for words with the precise number of matching letters. Use the suffixes as a filter. For example, if you found that the word "SUFFERING" had two matching letters, any words in the "-ing" suffix group would be excluded, but if it had five matches, chances are "-ering" is the proper suffix. This is usually, though not always, true. In the previous example, a match for "SUFFERING (5/9)" might be "FALTERING", but could also be "SUBMARINE".
To always hack successfully, go to the terminal, and save the game. Then, start the sequence. If you fail, just reload your saved game, and try again until you do it successfully.