Learn Swedish: Jag ber om ett glas vatten. - I ask for a glass of water.

In Swedish, you use frågar when you want to ask a question to get information. When you want to request an item or an action (asking FOR something), you use ber om. Since you are requesting the water, ber om is the right choice.

Why isn't there a word for "of" between glas and vatten?

In Swedish, when you use a container or a unit of measurement (like a glass, a cup, or a kilo) right before the substance it holds, you do not use a word for "of". You just put the two nouns directly next to each other, like ett glas vatten.

What is the dictionary form (infinitive) of the verb ber?

The infinitive is simply be. It is an irregular short verb, and to form the present tense, it just adds an r to become ber.

Why does om mean "for" here instead of "about"?

Prepositions often do not translate exactly word-for-word between English and Swedish. While om usually translates to "about", the verb phrase ber om is a fixed combination that always means "to ask for" or "to request".