There are two basic styles of chair lifts:

1) Straight stair lifts – where there is no curve in your stairs. These are the simplest and cheapest to install.

2) Curved stair lifts – where your stairs have a curver or right angled bend.

Here is an example of a curved stair lift

Curved Stair Lift

Curved Stair Lift (thanks to jingdianjiaju)