I'm not at all familiar with the topic either, but I've come up with quite a few more or less useful links and more important terms (Googling is all about finding the best terms).
But before I post them let me say that the 'old methods' where mostly used because there was no other way and most of them are very hacked or use some special mode (e.g. on the NES 'model 7'). So if you want to enter this area, good luck.
As second side note, you could always write your own software 3D renderer, but let me tell you it's not easy and would kind of defeat your purpose...
With the term 'fake 3d' I came across
this, which also lists different ways of doing things and links to other sites.
With the same term I also found
this, which is kind of short and the source is down...
While searching for 'model 7', I came across the well known and often used term '2.5D' and covers mostly all ways to fake some depth, see
this wiki article.
That article should give you quite a few other things to read and look into.
As addition maybe you can hope for an answer from Groogy, who's been doing something similar (but in Ruby), see
here.
Btw. if the scene is quite static and simply, you could also just use an image and scale the player as he moves and introduce some 'fake' boundaries. This is probably the easiest way to achieve a fake depth feeling and has been used in mostly all adventure games (King/Police/Space Quest but also Runaway (afaik) etc.).
