Example sentences
tā他dǎ打diàn电huà话gěi给shuí谁？
Who is he calling?
wǒ我dǎ打diàn电huà话jiào叫chē车。
I call for a taxi.
About this word
打 means "hit", 电话 means telephone, so the phrase is literally "to hit a phone". The 打 here is a light verb, one of those all-purpose action words Chinese leans on hard: 打篮球 play basketball, 打伞 hold an umbrella, 打招呼 greet someone, 打折 give a discount. No fist is involved in any of them. 电话 itself is 电 "electric" plus 话 "speech". Because this is a verb-object pair, you can slip other words inside it: 给他打了一个电话, "made him a phone call". The matching verbs are 接电话 answer and 挂电话 hang up.
The story behind the character
打
扌, a hand, on the left, with 丁 on the right giving the sound. Xu Shen wrote 打, 擊也: to strike. Since then 打 has gone feral in Chinese and attached itself to almost everything. 打篮球, 打车, 打电话, 打水. You do not strike a telephone, but the character stopped caring a long time ago.
电
The bronze 电 is a bolt of lightning, zigzagging down. The traditional 電 added a 雨 (rain) on top but kept the lightning below. Xu Shen wrote 电, 阴阳激耀也. The electricity in your phone began as the bolt splitting the sky.
话
言 (speech) plus 舌 (tongue). It just means spoken words. A phonetic character, no mystery.