Depending on context, all three of the verbs だ, ある and いる might be translated with some form of “to be.” So, what’s the difference between them?
だ is the literal translation for “to be” and also the simple form for present tense. Depending on the social situation it might be a good idea use the more polite form です instead. Someone named 夏子 (なつこ) could introduce him or herself like 「夏子です。」 which means “I am Natsuko.” Another example would be 「いちごがすきだ。」 (“I like strawberries.”)
ある and いる
“To exist” is probably a better translation for these two verbs. They can describe both that something exists at all (no matter where) and at a particular location (so it is there – that’s the connection with “to be”). The difference between them is that いる is used for living beings (humans, animals) and ある for everything else.
こうえんにはねこがいる。 (“There is a cat in the park.”)
ケーキがある。 (“There is a cake” or maybe “I have a cake.”)
だ, ある and いる are simple forms, used when talking to good friends or family members. When talking to others, you should consider using more polite forms as appropriate.