Besides the thought of giving the Sumo community back what one got from it, being oyakata is undoubtedly a good form of investing your money and saving a decent style of life. Many rikishi have been fighting for half of the time of their life, and when they retire at the age of 35 or more, they know lots about Sumo. Of course they will try to continue to do what they have learnt.
The requirements to become an oyakata are very high. First, you must be Japanese citizen. This rule was introduced to ensure that no foreigner can become an oyakata, let alone become an executive member of the Nihon Sumo Kyokai (and thus "de-Japanize" Japan's national sport). Unfortunately for the fathers of this rule they put it exactly this way: "Japanese citizen", forgetting the possibility of becoming a naturalized Japanese citizen. The former Azumazeki-oyakata (former Takamiyama) was the first one to take advantage of this loophole.
Second, you must have been a sekitori (paid rikishi). If you made it only to Makushita or lower, you have no chance to be an oyakata (you can of course be hired as trainer after retirement, but you will never become oyakata). Having been a sekitori is not enough. You must also have either a certain number of basho under your mawashi or have achieved a certain rank:
And third, you must own a Toshiyori kabu ("elder stock"), also called Toshiyori myoseki ("elder name"). These are the 105 licenses, connected with the names of past rikishi. When you become oyakata, you are referred to as "(name of the kabu)-oyakata." It is way easier to own kabu than to meet the above mentioned criteria! Actually, everyone can own one. But you may be kicked out of the Kyokai when you give one to a non-Sumo person.
You have three possibilities to achieve ownership: Either you buy a kabu, but the prices may well go up to 500,000,000 Yen for very prestiguos ones and are often only affordable because one's koenkai (sponsor club) has collected money. Or you get it as a present from your mentor or another oyakata. Or you inherit it from your father or father-in-law. For inheritance you have to meet a bit weaker requirements: Being only once in sanyaku rank (no need to complete that basho), have at least twelve basho as Makuuchi rikishi or at least twenty basho as Juryo and/or Makuuchi.
You don't even need to own a kabu, but only the right to use it. If an owner doesn't need his (because he is an active rikishi, an owner of multiple kabu or a retired oyakata) you may use his, if he gives it to you. This Karikabu ("rent stock") can be revoked at any time, however, so this isn't a very safe way to become oyakata. Borrowing was officially disallowed by the Kyokai for some time, but after kabu were "acquired" for symbolic prizes, it was obviously tolerated again.
An off-the-road way to become oyakata are the Ichidai toshiyori ("one generation elder"): You are allowed to continue as oyakata with the name you had as a rikishi. Apart from "having been an outstanding rikishi" there are no real criteria for Ichidai toshiyori. Until now only very great Yokozuna (those with twenty and more yusho) fell into consideration, and they usually won't have a problem meeting the aforementioned criteria. When the holder of an Ichidai toshiyori retires, the kabu cannot be passed on, but it simply fades. There are currently two holders, Kitanoumi and Takanohana. A third one, Taiho, had his mandatory retirement in 2005. Kokonoe (former Chiyonofuji) was offered one, too. Being raised in a very traditional heya, he turned down the offer and went the hard way acquiring a real kabu.
As the kabu are so rare and rikishi often retire too sudden to acquire a kabu in time, there were five Jun toshiyori ("junior elder") positions available until the end of 2006, earlier there were even ten spots. The rikishi -- who had to meet the basho/rank requirements -- did also continue under his name, but only for a limited span of time: Any rikishi who had not become Ozeki or Yokozuna was allowed to go on for one year (earlier: two years). After that they had to have a real kabu or retire. This rule was abolished when more and more kabu became vacant again. The "sister rule" is still valid for Yokozuna and Ozeki today; the have 5-years resp. 3-years grace periods. But they must have a kabu after that time, too, or they cannot go on. The former top rankers have never been counted to the official spots and also didn't appear on the banzuke as Jun toshiyori but as the highest ranked Toshiyori.
Being an oyakata, you can be affiliated with a heya and work there, or become a Shisho (leader of a heya; note: this term is also used in the meaning of "master", i.e. the one who recruited and trained you). But not every oyakata can become one. You must have at least 25 Sanyaku or at least 60 Makuuchi basho. Former Yokozuna and Ozeki can found their own heya regardless their number of basho, but they need to stay with their heya for at least one year after retirement. Shisho being close to mandatory retirement age (65 years) usually switch their more prestiguous kabu with an oyakata affiliated to the heya. As usual in the world of Sumo, switches, changes and even acquisitons of kabu base on mutual consent.