Typical grid connected installs of solar panels on homes need a couple of items to get them to work (it's not just lets slap some panels up there and wire it into the house). Solar panels are DC (direct current), your house is AC (alternating current), so a inverter is needed to create the AC current. Also that AC current needs to be synced to the same wave form that is being feed from the grid, another device (or sometimes packaged in the inverter). Then the new solar AC is then tied into your main panel, typically requiring another box. Also depending on the install, the panels might be electrically separated from each other (a good thing) requiring another device. Once connected, excess power from the panels will feed back into the grid and in some areas this will be credited back to you on your bill.
All said, this work needs to be done with a permit, typically with buy off from the power company on size of panels. Also for most DIY'ers, this is out of their scope of skill. Get some quotes from solar panel companies and electricians in your area to get an idea of what you are looking at.
Also look at the cost of the system and how much it is going to save you each month. Solar is popular here because power goes up to .30 a kWh depending on usage. But for my energy usage, I'm only sitting at .11 on average making solar unreasonable. My last bill was under $2 after energy program usage credits where applied.
The water pressure/flow analogy is, unfortunately, a common but very imperfect one. If we insist on using it, voltage is something like pressure and current is something like flow rate.
The key concept you're missing is that you need a circuit, not a single wire.
Voltage, like pressure in the pipe, is always measured relative to some reference point. If you were perfectly insulated otherwise, you could hold the hot wire all day and not do yourself any harm, as birds on high-tension wires demonstrate on a regular basis. In the electrical analogy, this is like a capped pipe, or a connection into a tank where the outside pressure is the same as that coming from the pipe. You can extend that pipe or enlarge the tank, but as long as the counter-pressure from the cap or surroundings equals the pressure coming in, no current flows. (I'm oversimplifying like mad, but that's inherent in the faulty model.)
Only when there's somewhere for the water, or electrons, to go will you get current. In a properly designed circuit, that's the neutral, which in the water analogy we can almost think of almost as a drain pipe. If we were talking about DC, you could think of the return/neutral path as a drain pipe; to make that idea work with AC we have to remember that the whole system is sealed, current flows both direction, and we get our current from water sloshing back and forth in the loop of pipes rather than any one drop of water flowing all the way around the loop.
It's current, not voltage, that does the actual work. But voltage ("pressure") is what causes current to flow.
(Of course if you poke a hole in the pipe and let current flow in another direction -- not just stopping at you but through you to a ground, for example -- the voltage will happily do its "work" on you, which is why it's dangerous. Ditto for short circuits, where the "work" goes into heating up the wire and potentially starting a fire.)
Your electric meter measures the current, not voltage. Until the circuit is complete and there's a path from hot to neutral (or, in the bad case, to ground), no current flows and the meter just sits there. When current is flowing, the meter uses a bit of the energy from that current to advance itself; a gentle current spins the meter slowly, a strong current spins it more quickly. In an AC system, the meter is set up to measure both directions of the "sloshing", or to act like a ratchet so it ignores one direction, and again you get a measurement proportional to how much current is being used.
As I keep grumbling, this analogy really is not a very good one, because it leads to misunderstandings like yours. I've forced it a bit farther to answer your questions... but really, the best answer is to stop thinking of electricity by analogy and start thinking of it as its own thing, and just learn how it behaves.
Best Answer
Pretend your panels are a water pump connected from a nearby pond (your roof) to a water tower (the grid).
The grid is a large reservoir that can simultaneously take and provide electricity. This is because there are multiple sources and destinations for the electricity.
If no one else was using electricity when you were providing it, your meter would not register outgoing electricity (credit).