I have heard that there will be some fees involved in the Lightning Network.. Who will be collecting those fees?

Potentially anyone who is running a Lightning-node.

Example:

Alice wants to send money to Carol, but Alice does not have an open channel with Carol.

But Alice has an open channel with Bob, and Bob has an open channel with Carol.

Instead of opening a new channel with Carol, Alice can route the payment trough Bob:

Alice — Bob — Carol.

In this scenario it is possible for Bob to charge a small fee.