Use с/со + Instrumental to say 'with' in the sense of 'accompaniment' and 'togetherness' as in 'bread and butter, bread with butter on it.'
Use с/со + Genitive to say 'from' (with на-nouns) and 'off'.
The variant со is used before щ and also before consonant clusters that begin with с-, з-, ш-, ж-, мн-, as well as before certain vowel-less stems, e.g. со льдом. The usage often varies from one gegraphical region to another.
Ї гулїл в пђрке с Ивђном Петрћвичем (Inst.). I was strolling in the park with Ivan Petrovich.
хлљб с мђслом (Inst.). bread and butter
Some of these с +Inst. phrases are often best translated with an English adjective + noun combinations:
рубђшка с длќнными рукавђми (Inst.). a long-sleeved shirt, a shirt with long sleeves
бутербрћд с ветчинћй (Inst.). a ham sandwich
Here are some examples of the use of the preposition с with Genitive case. The word Кџба, as well as the names of most other islands and many peninsulas, are на-nouns. Not all geographical на-nouns are islands, e.g. Алїска and, until its recently-won independence, Ukraine: на Украќне changed to в Украќне, which emphasized that country's new status.
Твћй учљбник упђл со столђ (Gen.). Your textbook fell off the table.
Ћн недђвно вернџлся с Кџбы (Gen.). He recently returned from Cuba.