Alright, so Firebase Firestore's offline mode is a neat feature that's automatically on for Android and iOS apps. But for web apps, you gotta turn it on yourself. You can do this with the `enablePersistence()` method.

For a web app, just add this:

firebase.firestore().enablePersistence()
  .catch(function(err) {
      if (err.code == 'failed-precondition') {
          // Multiple tabs open, persistence can only be enabled
          // in one tab at a time.
          // ...
      } else if (err.code == 'unimplemented') {
          // The current browser does not support all of the
          // features required to enable persistence
          // ...
      }
  });

When you enable offline persistence, the Firestore client SDK takes care of online and offline data access for you. It first checks the local cache when you try to get data. If the data isn't there, it fetches it from the server.

While you're offline, any write actions are queued up and will be executed once you're back online. Firestore also keeps local copies of changes, so your app can still work smoothly and give the impression of being connected.

To keep your data consistent, especially when multiple users are accessing and modifying it, you should use transactions and batched writes.

// An example of transaction
var sfDocRef = db.collection("cities").doc("SF");

return db.runTransaction(function(transaction) {
    return transaction.get(sfDocRef).then(function(sfDoc) {
        if (!sfDoc.exists) {
            throw "Document does not exist!";
        }
        var newPopulation = sfDoc.data().population + 1;
        transaction.update(sfDocRef, { population: newPopulation });
    });
}).then(function() {
    console.log("Transaction successfully committed!");
}).catch(function(error) {
    console.error("Transaction failed: ", error);
});

Firestore has this cool onSnapShot method that gets called whenever the state changes. It also gives you a 'metadata' object with 'fromCache' and 'hasPendingWrites' properties. These let your app listen and adapt to network status.

docRef.onSnapshot(function(doc) {
    var source = doc.metadata.hasPendingWrites ? "Local" : "Server";
    console.log(source, " data: ", doc.data());
});

These steps should help you handle Firebase Firestore offline data persistence. The Firestore documentation is a great resource for diving deeper into these processes, so definitely check it out based on what your app needs.