Pumps are your friend. Winter may not be.
Pumps can be man-power-driven. Parts can be made out of wood (I think.) Make sure to have the pumps drain back into another tile of aquifer, or you'll flood yourself out and probably throw your remaining dwarves into the drink.
If you have to, make do in log cabins until the caravans come, then buy what you need (preferably raw materials like stone) from them and sell anything you need to. I've never successfully used any method but the pump method. It's easy to understand and scaleable, where the collapse method generally isn't (it's limited by how many soil layers you have above the aquifer, so if it's too deep, you're done.)
Never tried double slit.
Pumps can be your friend, but learning how to pierce aquifers using just cave-ins will serve you better, you won't need to use all your wagon wood on a pump (or bring extra) or man it. In my experience a cave-in is also far quicker in play, and requires less micromanaging. Pumps should only be necessary if the aquifer is immediately below the surface, no dry soil levels at all, which I think is only possible in swamps, if even then, and even then only rarely.
For a 1-2 thick aquifer, 1-2 layers of dry soil are required, or 3 if the aquifer is only 1 thick and you want to do the whole thing underground, and not under the open sky. For a basic open-sky pierce of an aquifer that's just 1z thick, you need 2 layers of dry soil: the pictures on the wiki at
http://dwarffortresswiki.org/index.php/DF2014:Aquifer#Cave-In_Example are ok, although it has an extra, unnecessary dry soil layer above the aquifer (one of the brown ones). You can also avoid constructing the floor tiles in the last phase if you do the dig slightly differently. 2z of dry soil is preferable, since it lets you do the entire thing underground. Concentric ring cave-ins of thicker aquifers do require more levels of dry soil, however...
The "Single-pick challenge - Reawakened" thread included some aquifer pierce cave-in science. They were nearly alway done completely underground to be safe from aboveground undead wildlife and evil weather, and true to the name of the thread, people didn't bring any supplies beyond the 2 draft animals and 3 wood included with the wagon + a single pick. You would want to save the wood to be able to build a wall to block out even flyer access to your bunker, and to build workshops, so pumps were not reasonable, or even possible options. The science and explanations of the methods, complete with screenshots, start at around
reply #173: at first people still thought in terms of concentric rings or using pumps, but by the time the aquifer pierce discussion petered out at
reply #218ish or thereabouts, we'd figured out a way to pierce a 2-thick aquifer using only 2 layers of soil (similarly to before, just 1 would be enough if you didn't need the surface floor to act as a roof against wildlife&weather), without using any wood, all before the dwarves even get hungry (they can drink out of the aquifer and sleep on the soil floor)... and speculated on methods to have two alternating sites to repeat this method at, allowing piercing of arbitrarily thick aquifers, at least in soil. I don't think that theory has been tested, but if it works, 3+ thick aquifers may be piercable with just 1z of dry soil as well; if there's an upper limit, it would be starvation, and draft animal meat stews stave that off for quite a while. I'm not sure if testing 3+ thick aquifer pierces is that easy, mainly due to them not being nearly as common as 1-2 thick ones.
I keep telling myself (and others, in posts like this) that I really should write up the methods in that thread on the wiki. Although to be honest I'd like to repeat the tests for them on DF2015/2016 if it's delayed until then, or at least 0.40 before I do so (the experiments were done with 0.34)... and a good starting point would probably be to first add a minimalist version of the example already provided. Then a similar visual example of the concentric rings, then the methods from the thread... One of these days!
Regarding your current situation: Build a wooden palisade with optional moat and/or possibly cabins to live in until the caravans, or since you do seem to have dry soil, dig into the soil layers for rooms safe from the biting cold outside. Trade for stone and weapons-grade metals/ores. Brave the aquifer once more to gain access to stone, ores, caverns and magma.
edit: I made the picture series for the minimalist version of the example already provided, although I did add some Surface Fun to demonstrate why you might want to do the whole thing underground. It's getting late though, and I don't remember my DF wiki password, so I'll post it there tomorrow, hopefully. I also want to do a bit of arranging/cleanup on the aquifer article while I'm at it, and then the concentric rings should probably get a picture series too.