Summarize:

If this is your first time attempting to create an ambigram then choosing a word on the shorter side is a good idea. If you want to try something more advanced, pick a longer word.  Longer words pose more challenges as there are simply more letters that need to be made to look like each other. For example, a nice simple word to choose might be "BOOK" as it is only 4 letters. A more difficult word might be "TELEVISION" as it has 10 letters. Often, people will choose their name if they’re designing an ambigram for personal reasons so this is also an option. Just do this on a piece of paper with a pencil or use a word flipper. Write it so that the one spelling of the word is directly above the other spelling of the word. This will make it easier to analyze the word later on.  For example, if your word was ‘great’, write it out on a piece of paper and then directly below it write ‘ʇɐǝɹƃ’ lined up letter-for-letter with the normal spelling. It’s also a good idea to write the word in cursive and upper case. This lets you look at what letters may transform well into other letters. This process is the same regardless of whether you are creating a reversal ambigram or an upside-down ambigram as at the moment, you are just getting clear on which letters must transform into each other. One spelling of the word (right side up or up side down) should be on top of the other to make this much easier.  Make sure you are drawing lines down connecting letters from the regularly spelled word to the up side down spelled word.  You want to pair up the letters, ideally combine multiple into one. For example, for the word “great” you would connect ‘gr’ with ‘t’ with a straight line, then ‘e’ with ‘a’, then ‘a’ with ‘e’. Doing this allows you to pair up the letters and have a visual aid to what each letter needs to transform into when you look at the word from a different perspective. Combining letters is a way to make the ambigram more artistic but also much more difficult. Stick with just pairing individual letters up together if you want to keep it simple.  An example of how this works is that in the word ‘great’ the letter ‘g’ pairs up with ‘t’ (as these are the first and last letters). However, if you wanted to combine the letters, you might make it so the letter ‘g’ pairs up with the letters ‘a’ and ‘t’. This would mean that the letter ‘g’ will turn into ‘at’ when viewed from the alternative angle because you have combined the 'a' and the 't'. Combining letters is a bit more complicated so if you're just starting out, stick to just transforming 1 letter at a time.
Choose a word you want to turn into an ambigram. Write your word out normally, in capitals and upside down. Line up the two spellings of the word and connect the letters with lines. Decide whether any letters need to be combined into one.