I am very interested in outer space and the advancement of technology. I would like to get your opinion on what time-frame we can expect humans to start to colonize on the moon? I find this topic really interesting.
Bigelow Airspace did a study in which they claim various companies were interested in moon bases. They claim that inflatable moon bases could be in use by the late 2020s or early 2030s.
Russia plans on establishing a permanent presence on the moon in 2030.
Are these too optimistic? It is too early to tell. Technologically speaking, they are certainly possible, but whether or not they will be economically feasible is still a grey area.
There are not too many good reasons (I mean, economically justified, as opposed to mere awesomeness) to establish permanent bases on the Moon, let alone colonies. "Good" reasons include:
Science: the Moon is a good place for astronomy. The lack of atmosphere allows for a clear view, and there are craters at the lunar poles where one can benefit from permanent shadow (direct sunlight implies heat, which is a big issue for observations in the infrared band). Any place on the far side of the Moon will be good for radio-astronomy (a nice shield against emissions from Earth-based mankind).
Helium-3: this isotope of Helium is exceedingly rare on Earth, but relatively more abundant on the Moon (exact mechanism for this abundance is not really known, but there it is). 3He can theoretically be used for nice aneutronic nuclear fusion reactions (reactions which yield no free neutron as byproduct, thus much less resultant radioactive hazard). When fusion plants begin to work, and then are improved to also work with 3He fusion (which is harder to achieve than Deuterium-Tritium fusion), then (and only then) it may become economically sound to go mining on the Moon.
Transportation: the Moon can be a good step in the colonization of other bodies in the Solar system: it is much easier to send bulk material to Mars if you start from the Moon surface than the Earth surface, since lunar gravity is much lower than Earth's. This makes sense if there is some bulk material that is needed for a Martian colony, and is available both on Earth and the Moon.
Agriculture: on the Moon you can have all the sunlight you want, a lot of free space to grow crops, and controlled meteorology. You would need, of course, some sort of pressurized dome, but the gas can be extracted from the rocks, and plants can actually help in recycling the CO2 from the human colonists. The Moon as the basis for global human nutrition is a long term goal, unlikely to be relevant for a long time. It may help a lot, though, if some food must be produced and sent to some other base on a less propitious emplacement. (An agricultural Moon society is described in Heinlein's sci-fi novel "The Moon is a harsh mistress"; but sci-fi is fiction.)
It is unlikely that Moon colonization would begin for mere lack of space on Earth. It is way easier to establish a permanent colony in the Sahara, Gobi desert or Antarctica than the Moon. As long as there is space in Earth deserts (and space is not lacking there), then the Moon does not make much sense as a destination for pioneers.
Once the decision to go to the Moon is taken, it can be done in a relatively short time. At the time of the Apollo missions, the time frame from "political decision" to "Armstrong and Aldrin set foot on the Moon" was less than a decade. Technology from the 1960s was sufficient. In fact, the promise of Moon base "within ten years" has been made again and again, repeatedly, and it always failed to become reality, because of lack of money and political push, not because of any insurmountable technical issue. Shortly put: a Moon base, yeah, but what for ?
In practice, USA went to the Moon because they needed to beat the Soviets. Once they won the race, it became meaningless; they did a few extra performances (Apollo 11 to 17) then cancelled the show because of its price and falling audiences (Apollo 18 to 20 were never launched). What might motivate the USA to go again to the Moon would be a Chinese mission. If China sets foot on the Moon and begins to build a permanent base, then you can be sure that within 8 years (at most) some American base will be started too.