If you want to use Zoom on your phone instead of your computer, there are two different ways to do so. If you don't want to download the app, you can join a meeting by phone. Simply dial the number you received from the meeting invitation, and when prompted to add the meeting ID, use your phone's number pad to type it in. You will be redirected to the meeting after that.
If you want to join a meeting by video on your iPhone, download the Zoom Cloud Meetings application from the App Store. Once it is downloaded, open the app. It will take you to the homepage where there is a button that says Join a Meeting. Add the meeting ID, which you should have received via email by the organiser of the meeting. Type it in, and you will be added to the meeting. If you want to host a meeting on your phone, sign into your account. The homepage of the app will give you the options to start a new meeting, join one, or schedule one. Pick the one you want to do, and the app will set it up.