Ways to get your videos
If the title is released in your country, you just have to order it from a video shop and wait a few days. Most DVDs contain both dubbed and Japanese-with-English subtitles versions, but it is unwise to assume this without checking. A local release may not be exactly identical to the Japanese edition, but it will be reasonably priced, legal, a decent copy, and typically in hifi stereo/surround sound.
As a variant of this, you can order a video (for your own personal use) from another country via specialist dealers. This can be more costly (but equally can be a lot cheaper) and is more of a bother, but may well give you more choice in the way of subtitles or DVD "extras" etc. Or buy videos when you travel abroad. N.B. Customs duty may be payable.
As a further variant of this, you can get most anime (except the really old and obscure) from Japan on superior quality DVD (Region 2). This is very expensive (up to Y5000/Y6000 per 30 mins), plus charges. And it'll be (surprise?) in Japanese. (A few recent DVDs from Japan have English also.) There are also Japanese NTSC tapes, but being intended for rental, they cost as much as the DVDs. Within Japan however, one could often find used ex-rental tapes, distinguished by their attractive cheapness! (but perhaps not now). Bargain bin LDs were also sometimes seen.
Be aware that the temptingly cheap DVDs offered for international sale on Ebay are indeed too good to be true - they are mostly pirated editions of poor quality, unintelligible subtitles and unreliable delivery.
FansubsOnce upon a time, a few fans realised that the authorities would turn a blind eye to (or even legally sanction) the practice of making copies of imported anime and passing them around at the cost of tapes and sundries. As for the copyright owners, they couldn't care less what happened in a small way in some foreign country where nobody was ever going to license the product anyway, and "any publicity is good publicity." When US companies began to license anime programs, some conflict of interest arose. Fansubbers carried on regardless, usually stopping once a show was licensed. Few fans thought that fansub distribution was doing any harm, "just spreading the word".
Nowadays, almost any un-licensed anime, good or bad, is potentially available, often subtitled in English by teams of linguistically gifted and technically skilled fans, if you make the right contacts. Distribution (of questionable legality) now is usually by digital download of highly compressed files in divx and other formats. As for the wretched foreign licencees, they have to work very quickly to licence and distribute a good title, before half the fans who might be interested have downloaded a cheap soon-to-be-illegal copy or seen it at a convention. As almost any TV anime or video release is subbed and torrented within a week of release, this is becoming a losing battle. Once one used to wonder what the new season's TV anime was really like, but now you damm well know because you can download all of it subbed and look it it yourself.
The current trend (mid-2010) in a struggling overseas market is for new season anime to be simultaneously released for overseas streaming in subtitled or dubbed form. Thus instead of making an illicit download the fan only has to be patient for a week or so, or pay a modest monthly fee, in order to view the shows legitimately. However this does not seem to have deterred the fansubbers who push out their versions (sometimes stolen from the streaming services) regardless.
Signs are that the market for licensed anime DVDs in the US and the UK is collapsing, while the Japanese studios are strapped for cash and paying their staff peanuts. What role fansubs might have played in this I'll leave you to figure out.