How to Input Phonetic Symbols (IPA) in Google Docs

You can insert special characters by clicking "Insert" on the menu, then click the "Ω Special Characters", the choose "Latin" category from the drop-down menu, and then Phonetics (IPA) sub-category.

Insert Special Characters in Google Docs

There is a short-cut for inputting some IPA symbols which you use them frequently. Automatic Substitution in Google Docs similar to Auto Correct in MS Word. You can replace common acronyms, misspellings and other symbols. So you can set auto-replace for your IPA symbols, for example, "e<" for "ɛ", "o/" for "ø", "o>" for "ɔ" etc.

Automatic Substitutions in Google Docs