How would I say "I added ..." in Esperanto, in the context of editing a document? For example, "I added a picture of..."
I agree with other answers that aldoni is the appropriate word for this context, as well as in general context when you want to translate add.
Regarding edition in general, you can use redakti to translate edit, when your modification might just as well change and remove text, pictures, and so on in the document.
When you add (attach) a document to an email, you might prefer kunligi. For use cases involving a more intricate link, you could even use alligi.
More broadly, you might create words from whatever context suitable verb carrying the idea of a relation, prefixed with kun- or al-, depending on what you want mean precisely. Some roots which come to my mind are glui, meti, kroĉi.
In arithmetic, you might prefer adicii aŭ plusi.
Mi aldonis bildon de… [mia kato]… al la dosiero.