〜たびに: each time something happens
Connect a recurring occasion to what follows it. Distinguish this relationship from merely counting repeated actions.
Connect a dictionary form or a noun
この歌を聞くたびに、学校を思い出します。 means remembering school whenever you hear this song. Attach たびに to a dictionary form such as 聞く.
Nouns take の: 旅行のたびに写真を撮ります。 Do not join the words directly as 旅行たびに.
Pair the recurring trigger with its result
In 図書館へ行くたびに、新しい本を借ります, going to the library is the trigger, and borrowing a new book is the recurring result.
何度も本を借りました。 can simply report borrowing books many times. たびに additionally identifies the occasion linked to each repetition.
Keep the first verb in the dictionary form
日本へ行くたびに、友だちに会いました。 still uses 行く when describing past repetition. The final 会いました supplies the past tense.
For a single event, a construction such as とき or たら may fit better. First check whether you are describing what happens across recurring occasions.
Quick check: Does 旅行のたびに日記を書きます describe a practice repeated on each trip?
Show the answer and why
Yes. The person writes in a diary on every trip. Notice both の after the noun 旅行 and the recurring relationship.