Some affixes add a meaning to the word (such as the prefix ó) and some don’t. There are a few that you can easily look up the meaning of, but many of them don’t exist on their own in the dictionary so here I’m listing mostly ones that you can’t look up. All of these affixes have meanings, but keep in mind that affixes “often” or “sometimes” impart meaning and never “always”:

Prefixes:
al- adds the meaning of all/everything/whole.
Examples: aleiga (all of one’s possessions), almennur (universal, common), algengur (ordinary, commonplace), alveg (totally), alvanur (completely used to something)

all- is similar to al- but means “nearly” instead of “completely”. This is part of a collection of prefixes that are more like adjectives, and can be added more freely to change the degree of the word you’re modifying. The other ones are hálf– (half), jafn– (just as much as, equally), and lang– (long).
Examples: allavega (in all ways, anyway), allrahanda (all kinds), allsslags (every sort of), allskonar (of all kinds)
hálfviti (half-wit), hálftími (half-hour), hálfleikur (half-time), hálfunn (half-finished, semi-processed)
jafnvel (even, just as well), jafnstaða (equilibrium/break-even point), jafnmikill (just as much, of equal value)
langdvöl (long stay), langamma (“grandma from a long ways back” great-grandma), Langafasta (“long fast” Lent), langveikur (“having a long-term illness” and sometimes “terminally ill”), langvinnur (long-term, long-dated) langflest (by far)

auð- means easy or simple. It’s part of a collection that modifies the amount or difficulty of something. Some more are einka-/ein- (alone, singular), fjöl- (many), tor- (difficult), and van- (not enough).
Examples: auðvitað (naturally, of course, to be sure), auðþekktur (easily-recognized), auðskilinn (easily understandable), auðfundinn (easy to find, obvious)
einkvæður (monosyllabic), eingöngu (exclusively, solely, only), einkabarn (only child), einkatölva (personal computer)
fjölmargir (numerous), fjölskylda (“many relatives” family), fjölfatlaður (multi-handicapped), fjölmiðill (mass-medium and can also mean mass-media if it’s plural)
torveldur (difficult), torskilinn (obscure, difficult to understand), torfenginn (difficult to obtain)
vanmeta (underestimate, underrate), vantalaður (unspoken, remaining to be said), vannærðir (undernourished), vanræksla (“not paying enough attention” neglect, negligence)

for- means “before”, and goes along with endur– which means “after” and sometimes means the English prefix “re-” as in “doing something again”.
Examples: forskeyti (“affixed before/in front of” prefix), fornafn (“name before the second name” first name), forfaðir (forefather), forspjall (foreword), forstaða (head of something, ex. the head of a political movement)
endurnafn (“the name after the other names” last name), endurgjalda (“making someone pay after something has been done to you” payback), endurgjöf (“give comments after something has been finished” feedback), endursegja (retell), endurvekja (revive), endurtaka (repeat)

frum– means first.
Examples: frumsýning (premiere, first night), frumdráttur (“the first stages of something” draft, sketch), frumsemja (write an original composition), frumrit (original text)

mis– means variably/unevenly and the English prefix “mis-“.
Examples: misgóður (uneven, not consistently good), misjafn (unequal), misstíga (misstep), misskilja (misunderstand), mistök (mistake), mismunandi (different, variable)

sam– means together.
Examples: saman (together), sambúð (cohabitation, relations), samband (connection, relationship, union), samsetning (assembly, composition, compound), samfélag (community, society)

Suffixes:
-ing often means something born from an action and the English suffix “-ing”. However in Icelandic, -ing means nouns and not verbs (they have something else for that).
Examples: sýning (exhibition, performance, showing), bygging (a construction, building, structure), lýsing (lighting, illumination, description), sending (shipment, sending, transmission), blæðing (bleeding)
To explain, an exhibition and a construction cannot be made without some effort beforehand. Likewise, illuminating/describing and sending something also require some work. Bleeding is the most obvious, as you can’t bleed without having first some sort of injury or other problem. Thus they are all products of some sort of action. As for being able to see that they’re nouns and not verbs, that’s very difficult because in English they’re mixed up in comparison (you can say “there is a showing/building” but not “there is a bleeding/sending”). In Icelandic it’s much easier, you just know that -ing can be a noun ending. This was difficult to describe and I’m not sure I made things clear, so if you have a better way to explain then please let me know!

-ingur marks that the word has something to do with a type of person or that it is the name of an inhabitant/citizen of place.
Examples: Íslendingur (Icelander), kylfingur (golfer), útlendingur (foreigner), dýrlingur (saint), vitleysingur (idiot, lunatic)

-ó is used to shorten words.
Examples: menntó “menntaskóli” (high school/gymnasium), Sigló “Siglufjörður” (a place), púkó “púkalegur” (tacky), sleikjó “sleikipinni” (lollipop), strætó “strætisvagn” (bus)
Here is a list of some more. Some of these, like strætó and sleikjó, show up in Icelandic a lot more often than the full word.

There are many other affixes that have meanings, both in the sense that they tell you from what type of word the derived one is from (ex. something like “this is a suffix on feminine nouns that’s only on feminine nouns that were derived from masculine adjectives”) and in the sense we have in this post. Even if it may help sometimes, it’s mostly unnecessary to learn these because a lot of the words that contain these affixes can be looked up, and the common ones you’ll eventually understand naturally just because you see connections between vocabulary meanings.