While I think your question may be problematic to some because they are very weary of the "why" question, because physics can only go so deep, I recognize that it is hard to just accept a causal relationship between things that seem arbitrarily related, so lets try to look deeper.
A magnetic field is caused by a moving electric charge correct? The moving electric charge causes an increase in the electric field in front of it and a decrease in the electric field in back of it, and these changes create a magnetic field, but let's go back to the charge.
Let's imagine that this charge is moving extremely fast, at relativistic speeds even. Next to it and parallel to its motion is an infinitely long wire with current flowing through it, a lot of current too. Let's say that the electrons in this wire are moving just as fast as the electron, and in the same direction. We could even imagine them with race helmets on, racing each other off to infinity.
Now this wire is electrically neutral, for every electron in the wire there is a proton, so the electron traveling alongside should feel no pull towards the wire or a push away. However, this is all from our perspective. To us the electrons are moving fast, but what about to them?
According to relativity, they have every right to say that they are not moving. What looked like racing hats to us were actually top hats, and they were sitting down having some tea while we zoomed by at nearly the speed of light. Now we would look sort of funny, because the effects of relativity cause us to look squashed. This is important, because we would not be the only things zooming past the electrons.
The protons in the wire as well would be zooming past them as well. The same relativistic squashing happens with them, but this time it's more important. The relativistic length contraction not only squishes the protons, but because it is a whole column of protons moving past them, the column squishes as well, increasing the positive charge density of the wire. The electron feels the effect of this increased charge density as a pull inwards and so it drifts closer to the wire.
We see this in our frame as well and are perplexed, why would the electron feel a pull from the wire? We see no excess charge in the wire, so we ascribe this effect to a different force, the magnetic force. However, from the electrons reference frame, this behavior is perfectly normal, the protons moving past him are closer together than the electrons standing still and the electric force from the wire pull him closer.
This is kind of what magnetism is, electricity's compensation for relativity. For if magnetism didn't exist, we would see the electron attracted to the wire, for no explainable reason. Magnetism is sort of the relativistic form of electricity.
As for them interacting and causing each other, this must happen or else other laws of physics could possibly be broken (or you would have a meaningless thing like a force from nothing). This is a comforting example of how a part of physics holds itself up by itself.
Can some one please explain to me why electricity flowing though a
copper coil generates a magnetic field or where I could possibly find
that information?
An electric current (a flow of electric charge) has an associated magnetic field regardless of the material (or space) the flow occurs in. This is a fundamental part of electromagnetism, rooted in observation, and quantified in Ampere's Law.
I wish to emphasize that this phenomenon is considered fundamental in nature, which means there cannot be a "more" fundamental explanation (if there were, electromagnetism would not be fundamental).
Best Answer
Here is an approximation of what you are trying to do. The magnetic field inside a solenoid is given by (from Wikipedia) $B={\mu}nI$ where ${\mu}$ is the permeability of the medium (presumably water in your case), $n$ is the number of turns per unit axial length, and $I$ is the current. The maximum value of $n$ is determined by the thickness of the wire you are using. This vendor sells magnet wire as thick as 12 gauge, which for a single layer wrapping yields $n=468$. The permeability of water is very close to that of vacuum, so use ${\mu}=4{\pi}{\cdot}10^{-7}$ $H{\cdot}m^{-1}$.
Achieving your minimum desired field of 0.1 Tesla requires a 170 Amp current which is probably well beyond the safe operating range for 12 gauge wire. Now this is an engineering problem. You could look for a thicker wire and also wrap multiple layers to reduce the required current. If the water is flowing that will help keep the wire cool, but being submerged demands careful consideration of electrical isolation. Here are some epoxies for potting electronics, though I suspect there are many other options available. Hopefully the links provided help illuminate what keywords to use in your research.
Once you have an idea of what kind of wire to use (and its resistance), and also the max current you'd like to run, you can use $P=I^2R$ to estimate the power you will need. Then you can start shopping for a DC power supply.
A 1 Tesla field is huge!
To the senior members: I apologize in advance if it was in bad taste to link to vendors.