i think i've answered this question before, but i can't find the post, so i'll just answer it again!
i typically first decide what words i might like to include in the term. for example, while coining floracornic, i knew i'd want to include 'flowers' and 'unicorns' in the term itself. from there, i determine whether i'll be using the english word, as i did with '-corn' for 'unicorn', or a related word or root word, as i did with 'flora-' for 'flowers' ('flora' meaning 'flower' in latin and being used in english to refer to the plants of a region). i might also choose a translation of the word into another language, a synonym, a scientific name, etc. i usually list a handful of options to use for each word.
then i determine whether the words i've chosen will be best as a '-gender' term or a monolexic term ('monolexic' refers to genders that don't use the prefix or suffix 'gender'). for example, if you're coining an aesthetigender, you might go with the suffix '-aesic'; if you're coining a gender that you feel needs three or so words included in it, you might go with a monolexic term to avoid the term being too long; if you've only got one word you need to include in your term, you might go with the '-gender' suffix. i recommend checking out pupyzu's suffixes carrd if you aren't sure what suffix to use!
i just start combining things in various ways until i come up with something that i feel looks best, rolls off the tongue nicely, etc. i might drop a word i want to include if i feel like it's not feasible (such as my term 'plushlichten', where the only root words included are 'plush' and 'licht', meaning 'light'), or maybe i'll find a way to combine two words into one (such as my term 'lepidere', where 'lepid' refers to both butterflies and moths). your term doesn't have to include every relevant word if you don't like how it looks/sounds when it does!
i also always do a preliminary check to see if the term i've come up with exists elsewhere using my guide to finding terms by name. i usually just use step 2, the googling step, since it's the most comprehensive! you don't want to accidentally use the same name as someone else if you can help it.
this looks like a lot, but honestly, explaining it in-depth makes it look less fun than it is. just go for it! grab a few root words and combine them randomly until you've got something you like.