1) What values does a physical Kanban board offer?
Visualize all team work using a very low-tech, low-budget tool while promoting face-2-face communication between team members, collaboration, and team-based problem solving. Physical Kanban boards have been around since the 80's and continue to be used by many, many organizations to help with work visualization, staying on track, and keeping teams of people focused on solving the right problems. Digital boards are becoming more and more popular with fairly flexible offerings from Jira, Rally, VersionOne, etc, but at the end of the day they all replicate the exact same behaviors you can drive on a team using a physical board.
2) How to make and use it? I mean, who is going to cut paper to make "card", write down on the card, etc..?
3M and numerous other companies make stickies. Index cards with tape work fine too. Anyone that learned to write can create a Kanban card. If you have $50 you can build a pretty sweet kanban board + tickets in very little time.
3) Is it really worth the effort?
It takes less than an hour to create a physical kanban board. All you need is a surface, some lanes (you can draw them with a marker of use tape), cards, and something to write with. If an hour invested that helps promote collaboration, work transparency, and team-based problem solving for the life of a project or team seems like a large investment, you probably have deeper issues to fix first.
The hard part is getting the team to own the process and working agreements the kanban board represents ;). Trying to create a kanban board is often the first step to achieving these behaviors, however.