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An ambigram is word design that when viewed from a different angle is still understandable as the same word or as a new word. While it is possible to create one through calligraphy, the majority are typographical. This means employing a word processor or art software to create the word on a computer. Ambigrams make for popular logos and are often used as tattoos.
In order to be an ambigram, the word design has to be stylized. This means incorporating some kind of calligraphic or artistic style into the word. This can involve looping fonts or altering the shapes of letters so they are understood one way up, but form different letters when flipped left-to-right or upside-down. If there is no style in the presentation, then it is not an ambigram.
There are several different types of ambigram. One of the most popular or recognized is the rotational ambigram found on websites and graphics. The rotational is a form of graphic design, which has the word design rotate after a specific number of seconds. The word is usually stylized so that it reads the same both ways up. The word "ambigram" itself is often used as an example of this kind of word design, as the ‘a’ and ‘m’ at the beginning and end can be stylized so they seem to swap places as the word rotates.
A variation on the rotation changes the actual word. This often works best if the two words formed in rotation are opposites of one another such as ‘angel’ and ‘devil.’ Such rotations can rotate physically through graphic design or be presented without movement, but if the picture was turned, then the new word would form.
The third kind is the palindrome ambigram. This has also been called the ‘palindrogram’ by some. Rather than rotating on a point of axis or being flipped upside-down, the palindrogram flips from left-to-right, either by changing the picture on a computer or by using a mirror. As with all other palindromes, such as "A man, a plan, a canal, Panama," all palindrograms read the same back to front as front to back. Stylization must be present with the palindrogram or it will just be a normal palindrome.
Another alternative is the perceptual shift ambigram. This type of word design does not require mirrors or rotation. Instead, as with an optical illusion, the viewer is required to shift his or her perception of the word or words so that they take on another form. For example, the word ‘magical’ could be written so that with a little tweak of perception it turns into ‘illusion!’ or even ‘musical.’
The ambigram has become a popular area of graphic design. There are websites and publications dedicated to them and a number of competitions. These competitions tend to be focused on particular themes or challenges such as palindrograms. The ambigram logo is also a popular style for word tattoos alongside Chinese characters, Arabic and Hebrew scripts.
Ambigrams are amazing. I don't think that there is any way to create one in "word processing" software like you mentioned, but you can create one on-line.
The site that seems to have the best variety and highest quality ambigram artwork is FlipScript, although I have tried a couple of words on their web site that could only create a circle ambigram.