One of the first things taught in anthropology classes is that presents exchanged in a given society hardly ever come for free. When someone gives another person something, that always entails some sort of obligation. Acts of giving and receiving are hence highly sensitive social endeavors, and so is the language of these acts.
In contrast to the English dyad of "give" and "receive," in Japanese we are dealing with a triad of verbs, consisting of あげる (ageru), くれる (kureru) and もらう (morau). The reason why we need three rather than two is that Japanese additionally distinguishes whether a speaker gives or is given to: When I give someone a present, what I do is プレゼントをあげる (purezento o ageru), whereas when someone gives a present to me or someone close to me, that is a case of プレゼントをくれる (purezento o kureru).
In more formal situations, あげる, くれる and もらう are regularly replaced by their polite counterparts 差し上げる (sashiageru), くださる (kudasaru) and いただく (itadaku), respectively. As for more casual acts of giving, there is the verb やる (yaru). It is used when a "giver" is in a markedly higher position than the receiver or has a very close relationship to them. When giving a present to my little brother, for instance, I could say 弟にプレゼントをやる (Otōto ni purezento o yaru). やる is also a good choice when giving to nonhuman subjects, as when watering your plants, 水をやる (mizu o yaru, "give" water), or feeding the cat, 餌をやる (esa o yaru, "give" food).