1. Explain it simply
到底 has two uses. In a question it means 'what / who ... on earth', pressing for a clear answer.
In a statement it means 'in the end / after all', giving the final result after a process.
Question order: Subject + 到底 + question word or A-not-A form + ...？
Statement order: Subject + 到底 + verb phrase, often with 还是: 他到底还是来了.
到底 is more colloquial than 究竟.
2. Show examples
你到底想不想去？
Nǐ dàodǐ xiǎng bù xiǎng qù?
Sandhi:Nǐ dàodǐ xiǎng bu xiǎng qù?
Do you want to go or not, in the end?
question use, presses for an answer
这件事到底是不是真的？
Zhè jiàn shì dàodǐ shì bù shì zhēn de?
Sandhi:Zhè jiàn shì dàodǐ shì bu shì zhēn de?
Is this matter true or not, really?
used with the A-not-A form 是不是
等了很久，公交车到底来了。
Děng le hěn jiǔ, gōngjiāochē dàodǐ lái le.
After waiting a long time, the bus finally came.
statement use, meaning 'in the end'
3. Share a tip
In a question 到底 asks 'on earth'; in a statement it means 'in the end' - either way it goes before the verb.