Your club follows your sign-in, not your phone
Your club is tied to how you sign in (Apple or Google), not to a specific phone. Sign in on the new phone with the same account and your club comes with it, full history intact.
There is no guest mode: a club can only be reached through the Apple or Google account it's signed in with, so the account is the thing you move.
The one thing to know before switching between Android and iPhone
Apple sign-in only works on Apple devices (iPhone, iPad, Mac).
Google works everywhere (Android, iPhone, iPad, Mac, PC).
So Google is the bridge between an Android phone and an iPhone. As long as your account has a Google connection, you can sign in on either one.
Before you switch (do this on your old phone)
If you already sign in with Google: you're set. Skip to the next section.
If you only sign in with Apple (the usual case on iPhone): add a Google connection while you still have the old phone. Go to Settings → Connections → Add Connection → Continue with Google. Pick a Google account you don't already use for another ESMO club.
On your new phone
Install ESMO from the store (Play Store on Android, App Store on iPhone).
Tap Continue with Google (or Continue with Apple if both phones are Apple) and choose the same account.
Your club loads with everything as you left it.
Moving between two phones of the same kind
Android to Android, or iPhone to iPhone: nothing special. Just sign in on the new phone with the same account you already use.
Important
Add the Google connection before you lose access to the old phone. If you can still sign into the old device (or any Apple device for an Apple account), you can always add it later, but it's easiest to do it before you switch.
One account, one club. Don't sign into a Google account that already has its own ESMO club, or you'll be switching to that club, not moving yours. See the Single Account Policy article.
FAQ
I switched from iPhone to Android and I see a brand new club.
On Android, Apple sign-in isn't available, so signing in started a fresh Google club. Sign out, then sign back in with the Google account that's connected to your original club. If you never added a Google connection on the iPhone, sign back into your iPhone (or any Apple device), add Google under Settings → Connections, then use that Google account on Android. Still stuck? Message me in the in-app chat and I'll sort it out.
Does adding a Google connection change anything about my club?
No. It just adds another way to sign into the same club.
I have an iPad and an Android phone.
Same rule: Google is the bridge. Add a Google connection, then sign in with it on both.