Here are some of the more common such suffixes. Which of each pair is used depends on the word being suffixed in accordance with the rules of vowel harmony.
-ja/jä : agent (one who does) (e.g. lukea "to read" → lukija "reader")
-lainen/läinen: inhabitant of (either noun or adjective). Englanti "England" → englantilainen "English person or thing"; Venäjä → venäläinen "Russian person or thing".
-sto/stö: collection of. For example: kirja "a book" → kirjasto "a library"; laiva "a ship" → laivasto "navy, fleet".
-in: instrument or tool. For example: kirjata "to book, to file" → kirjain "a letter" (of the alphabet); vatkata "to whisk" → vatkain "a whisk, mixer".
-uri/yri: an agent or instrument (kaivaa "to dig" → kaivuri "an excavator"; laiva "a ship" → laivuri "shipper, shipmaster").
-os/ös: result of some action (tulla "to come" → tulos "result, outcome"; tehdä "to do" → teos "a piece of work").
-ton/tön: lack of something, "un-", "-less" (onni "happiness" → onneton "unhappy"; koti "home" → koditon "homeless").
-llinen: having (the quality of) something (lapsi "a child" → lapsellinen "childish"; kauppa "a shop, commerce" → kaupallinen "commercial").
-kas/käs: similar to -llinen (itse "self" → itsekäs "selfish"; neuvo "advice" → neuvokas "resourceful").
-va/vä: doing or having something (taitaa "to be able" → taitava "skillful"; johtaa "to lead" → johtava "leading").
-la/lä: a place related to the main word (kana "a hen" → kanala "a henhouse"; pappi "a priest" → pappila "a parsonage").