As mentioned by ranpinch, "יותר" is comparative ("more than"), whereas "עוד" is "additive" ("more of").
עוד is used in other constructions and meanings (mainly "still" - אני עוד שם = "I'm still there"), but it'll be best to leave it for now if you're a beginner as it's mostly colloquial Modern Hebrew, except for the "still" meaning.
If you know some French... יותר is like "plus", and עוד is mor like "encore".
אני צריך יותר אנשים, [FR] il faut plus de personnes, [ENG] I need more people
אני צריך עוד אנשים , [FR] il me faut encore des personnes / quelques personnes de plus, [ENG] I need some more people / some additional people.
עוד can sometimes be replaced by נוסף.
You can also combine them: הוא עוד יותר גדול , [FR] il est encore plus grand, [ENG] he is even taller.
In the negative :
אני לא רוצה יותר = אני לא רוצה עוד I don't want anymore / I don't want any longer.
אני עוד לא רוצה I don't want yet.