First the why, to get out out of the way.
Part 1) Why Colonize outer space at all?
A: To get human life/civilization off this planet, as only the spreading of human life as far & wide as possible can increase the chances of survivability of the human race as a whole, given that on a large enough scale, 'local' disasters can include wiping out an entire species on a given planet.
Added Benefit: Advances in technology required to do this completly will advance our knowledge and most likely increase our quality of life (Space-born technologies i cna think off of hand: the modern refrigerator, cell phones, and the wave front technology used for advanced laser eye correction surgery)
Part 2) If I except that, why Venus?
A: Near-earth mass & size and already present atmosphere offer great promises towards eventual habitability with out involving being permanently living in a giant super-building.
Disadvantage: It's current atmosphere is actually the biggest hurdle in making it habitable. Explained in depth below.
Now that the Q&A is out of the way, let's get on with the 'how'.
Fortunately, Venus offers what may be the least expensive, but also potentially the slowest going, method of terraforming: Get life to do the work for us. The temperature and pressure on Venus are truly, truly extreme. Which is where creatures called Extremophiles come in handy. Namely, thermophiles and acidophiles (which some times go hand in hand).
But the ones currently on Earth are not tough enough for our needs. Oh, there might be a few species that can be collected from Black Smoke volcanic vents on the sea floor which would survive in the upper atmosphere near the poles, but we want better than that.
So we turn to an age-old technology that takes advantage of evolution. We call it 'breeding'. We collect the microbes from appropriate volcanic vents form around the world (to get as much genetic variation into the mix as possible), and create large tanks that simulate the conditions of the volcanic vent areas. These tanks will also need various controls and technologies for creating ideal situations for fast-tracking evolution to give us what we want.
The tanks would be used to create a varied environment, with one end of the tank being hotter than the other. The hotter end of the tank is where nutrients would be introduced, so that microbes better able to survive in a hotter environment would have better access to food. with such a direct ration of advantageous trait to survivability, as soon as the hotter end of the tank is heavily populatedyou can start cranking the heat up on that end slightly (note, it woudl be very important to mix the distribution of microbes before doing so, in case the small temperature change is to much for that generation to handle)
This is an expensive proposition, but like many extreme experimental technologies, simply doing this woudl likely provide us with new raw data regarding biology. And it would likely take a long time before reaching the point where they can survive on the surface of Venus anywhere, by temperature alone. More likely is the possibility that we'll eventually reach a stagnant point, where no matter how long we let them sit, no mutations or other genetic variations will allow the microbes to get any closer to the food source/hottest point in the tank.
Fortunately, Acidity and pressure are already covered by the living conditions they are already in here on earth.
Once you have a stable population in each of the tanks, you now take samples from every tank (as they might have adapted to higher temperatures via different mutations), and mix them in a new set of tanks. It is very important to keep your first set of tanks maintaining a population, in case anything goes wrong in the stage 2 tanks. Then you won't have to fall back as far (consider it a 'save point').
The thing to adjust here is food. Namely, you start introducing compounds that are in Venus's atmosphere that are not already in their own environment. Once you've verified that these new compounds do not act poisonous to the microbes, you slowly increase the amount. Then you start reducing the nutrient compounds that are not found in Venus's atmosphere.
Again, making a graduated situation is ideal, but may not be necessary in this case. Eventually you should have a set of microbes that have adapted to this new set of nutrients, surviving solely off of nutrients found in abundance on Venus.
Now the tricky part. Disclaimer: there is a very good enough chance that at these preasures & temperatures Venus atmosphere & water interact in ways that make my ideas not workable as is. Stage three is getting rid of the water. Venus is a very dry planet. I would recommend gradual slopes placed through out the tanks, followed by introducing Venus atmosphere at the top of the tank, before withdrawing water at the bottom (into another pressurized tank of course). Or vice-versa, if the specific gravity of Venus's atmosphere is higher than water's, at that temperature and pressure. Possibly some other method You want about 50-50, assuming that they won't quickly dissolve into each other.
Keeping with that assumption, you'll also need a small wave motion generator, and some divots and bumps on the slopes. Most of the time you keep the wave action very small, to create continuously moist surfaces that are exposed to the Venus atmosphere mix, and infrequent but regular larger wave sets to push water into divots that would collect it and hold it. If creating this tidal pool structure is possible, you should be able to just let it run indefinitely, until you have microbes living exclusively on the dry sections. Keep reducing water levels and adding more dry atmosphere slowly, there still be a humidity factor for the microbes living outside of the wet zones.
If the Venus atmosphere at the water mix freely, then no graduation is available. Instead, just slowly increase the concentration of Venus Atmosphere compounds in the water until it reaches such a high concentration that it will no longer dissolve. It shoudl form some sort of bubbles (at the top or bottom of the tank). And then patience becomes key, a waiting game to see how long it takes microbes to migrate to the areas where there is no water. There will be less food imperative as the microbes will have already adjusted to eat the same compounds which are very abundant in the water. Space/room seems to be the only adaptive imperative in that situation.
So that third, trickiest part is the final biological hurdle. Once we have microbes surviving in a Venus atmosphere, even if only in certain conditions (say, over the polar caps at high-ish altitudes) we can make sure our next Venus mission includes releasing spores in the appropriate locations, while we continue breeding the microbes to fit more and more areas.
So a lot of work, mostly in the form of time. But, it is *relatively* inexpensive in terms of money, compared to terraforming other worlds. And of course, this is only stage one. The purpose of stage one is to start taking the sulfur out of the atmosphere, and other greenhouse compounds. Any greenhouse gasses produced in that process, we breed something to eat that too, if at all possible.
At some point, we may be required to flat out genetically engineer microbes, but that's a few centuries off I'm guessing. At least. And this whole process may take millennium, during which time we might also colonize other worlds. But as long as we keep sending in biological agents to do our work for us, we can keep it as a back ground project, to eventually seed with life forms that will free up oxygen, and then basic multi-purpose plants in several waves, then we can start full scale colonization with out having to live in giant arks permanently. Really, beyond getting this process started, it's hard to describe what we'd do, because there are so many possibilities of technol;ogical advancement.
Or maybe we'll get things started on changing Venus, and something will happen that sets us back to the stone age, and it takes 5 thousand years for us to really look at Venus again. And we re-evaluate again at that point. But no matter what the eventual path we take, creating possibilities is better than closing them. So let's open up this path.
here are some links to some rather relevant sites, though they have some differing ideas on how to go about things.