5) You can also draw a diagram of the forces exerted on each point of the Earth, considering the gravitational pull from the Moon *and* from the Sun. This is laborious, but given the recipe it's just repeating as many times as you need. If your programming skills are adequate, you can write a computer program to draw it for you. You should end up with something like this: http://en.wikipedia.org/wiki/File:Field_…
Notice there's a difference between having only the Moon pulling or having both the Sun and the Moon pulling; see this diagram: http://abyss.uoregon.edu/~js/images/tide… Notice how the arrows pulling "inward" means that the water is pushed aside ("downards" for someone sitting at that point on the globe) and the arrows pulling "outward" means that the water is pushed together (giving the impression of a high tide at that point of the globe).
This point gives an explanation to why there are *two* high tides and *two* low tides during one day (the time it takes the Earth to complete one rotation).
Anyway, this is a suggestion for your discussion.
But if you REALLY want to convince your friend, there's a much better way: DOING IT YOURSELVES. In fact, I wouldn't be surprised if this was something that teachers would make high school students do as part of their science coursework.
Really, until you take the time to measure the time at which the water is high and low (in a large lake or sea shore), and the time at which the Moon rises, sets and passes overhead (the time at which it rises highest in the sky); and after you've collected that data for a few days and start comparing them; your friend will have a hard time believing you. It's best that you take notes of the times at which the Moon rises and sets, since for a good portion of each month the passage of the Moon in the meridian happens during daytime and so you won't be able to measure it.
Doing stuff and looking at what you two have done is the very best way to convince yourselves of it. Now the summer months are coming in, you should have a great opportunity to do it over one or two months. It doesn't take much time; it just needs to be done regularly.