The adverb 顺便 indicates that two actions are happening at the same time or that one action happened while another action was taking place.
In a sentence, it is placed before a predicate which is expressed by a verb.
Examples
请顺便把垃圾带下楼
If you're going out, take out the trash, please
qǐng shùnbiàn bǎ lājī dài xià lóu
我到了上海,顺便去看望了小学老师
When I arrived in Shanghai, I visited my primary school teacher
wǒ dào le Shànghǎi, shùnbiàn qù kànwàng le xiǎoxué lǎoshī