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[lotopius]

I have no more water on my map.
Like no water; at all.
The combination of dwarfy drowning traps, !!science!! with screw pumps and irresponsible irrigation have lead to the evaporation of all the water I have available; including the one in the caverns.
I have a few rain collectors outside; but it takes over 3 years to fill one completely; and several times the water evaporated before it was able to reach 3/7.

The question is; is there a faster way to obtain water?

[PTTG??]

Make a smaller, entirely underground water collector, so that it will get to a safe depth more quickly.

[Hans Lemurson]

What climate are you living in?  If it ever freezes in the winter, then you can use magma to cause melt/re-freeze cycles to generate unlimited amounts of water.

If it's hot or scorching, then You'll have to transform every "murky pool" on the map into a water-collector (you've probably already done this).  In environments where any level of water is subject to evaporation, the most important thing to concentrate on is getting it underground ASAP after it falls from the sky.  Set up water-collection one level below the murky pools so that rainwater that accumulates in them immediately flows out of the pool and into your collector.

If your environment does neither of these things, and your woes are mainly because you "killed" all your water-sources, then your only recourse would be to try to "revive" these water-sources one by one.  "Killing" a pool means its average water-depth goes below 2/7, and so is slowly subjected to evaporation.

Two additional questions: 
-What are your current water-reserves?  This will affect what options you have.
-Have you examined all 3 caverns and determined then none of them have any pools of water which connect to the edge of the map?

[vipre01]

dfliquids

[lotopius]

How are you supposed to make rainwater go underground?
From what I understood; each time "rain" falls onto a tile, it creates a 1/7 spot of water at that place; but 1/7 water never displaces unless a pump is used; so I can't move it to an underground location unless I make it fall on an already 3/7 tile of water wich removes the necessity to actually make it go underground, since it stops evaporating at 3/7.

[mrbaggins]

First, water stops evaporating at 2/7, in normal or cold climates.

Second, what you do is skim off everything above that (making sure it doesn't go under) so that the pool is never empty (which is very difficult to get refilled). This way, every bit of rain adds 1/7 to whatever square it hits. A decent rainfall will fill a 2/7 pool right up (and a single channel while raining will not be able to empty the pool).

So make a big reservoir underground, link it up with floodgates to pools, and whenever they're starting to get full, pull the lever. Once they're down to 3/7 or so, start getting ready to shut the floodgate.

[Buttery_Mess]

You think that's bad, I've got no water at all. Just an underground magma sea. No rain, no river, no acquifer, just lava, rock, and dry mud. Also, no trees or plants.

[Hans Lemurson]

How are you supposed to make rainwater go underground?
From what I understood; each time "rain" falls onto a tile, it creates a 1/7 spot of water at that place; but 1/7 water never displaces unless a pump is used; so I can't move it to an underground location unless I make it fall on an already 3/7 tile of water wich removes the necessity to actually make it go underground, since it stops evaporating at 3/7.

The "make rainwater go underground" method means that you set it up so that once the whole pool-bottom is covered in 1/7 water, all additional water that takes the form of little 2/7 tiles that goes skittering around in the pool then flows out of the pool and into the collector you've dug next to it.  It is not "make it rain underground", it is "take water made by rainfall and keep it safe from the scorching rays of the sun".

However, it seems that you're probably in a temperate zone, since you're not experiencing "full" pools of water drying up (meaning that that method won't be too helpful), so as long as you can restore some of your existing pools (start small) to above the "critical level" (no 1/7s anywhere in it), then you can start collecting rainwater again in earnest.

So long as you have SOME water in reserve, you'll probably be able to restore your pools.  I would actually be interested in trying-out the great engineering-challenge that would entail, if you'd be willing/able to upload your save somewhere (I'm not exactly sure how to upload saves...).