A
common question when new to texture mapping, is
what resolution should textures be? This is assuming
that you are going to be making your own in a
2D package, such as Photoshop, either from scratch
or from a scan. Well, the first thing to do is
ignore dpi settings. All you care about is the
pixel by pixel resolution of the image. If you
are scanning an image, most scan software will
have you specify dpi. A 4"x5" photo
scanned at 300dpi will yield a 5MB 1200x1500 pixel
image. But once the image is scanned, you will
no longer concern yourself with it's dpi setting.
So lets say we did scan the aforementioned image
and now have a 1200x1500 pixel document. This
is going to be much larger than necessary for
most applications. And using textures which are
too big simply slows down your render time and
gives your scene a bigger memory footprint. (meaning
the amount of RAM needed on the machine to render
the scene). If your memory footprint is bigger
than the amount of RAM on the system, the machine
will need to use space on your hard drive, known
as 'swap' space, and when you begin swapping,
things really slow down... and then you're on
the verge on not being able to render the scene
at all... not a good thing.

So,
here's a simple example: you need to texture a
doorway. Well, in the above image, the doors are
a single NURBS plane, as they do not need to open.
You need to ask two questions... what is the closest
the doors will get to the camera, and what is
our final output resolution? If the above example
IS the closest we will get to the doors, then
let's also say we are rendering at 640x480.
Since
100% of the door is in the frame, then what percentage
of the frame is it filling? It looks like it is
about 1/3 the width of the frame, which would
be 213 pixels. Maya, however, prefers textures
to be in multiples of 64, so the best horizontal
size for the texture would be 256. Maya also prefers
textures to be square, so our texture should be
256x256 pixels. It is not 'necessary' for them
to be square, however and I often use non-square
textures. Its just that a 256x128 texture will
use up the same amount of memory as a 256x256
texture when rendering. So now that this is all
figured out, we can go to Photoshop and reduce
our texture to the correct size. It is a good
habit to have higher-res versions archived in-case
you want to render your scene at a very high-res
for print, for example.

So
above is the texture we're going to put on the
door. Its too big, but we'll archive it.

So
here we go... 256x188 pixels.

Looks
ok in Maya... But watch out. Maya blurs imported
file textures a bit by default, so even though
you we're responsible and determined the optimum
size for your texture, it will look a bit blurry
in a rendering. Select the File texture in the
Multilister, open the Attribute Editor, and in
the Effects folder, set the Filter setting to
'0'.... it defaults to 1. This can be useful if
your texture is too small. The 'Filter' can blur
your texture to reduce pixelation, but if your
texture is the right res, be careful.
So
after all this, we're ready to render...

Now
this example may seem simplistic, but that's the
point. It is never really gets any more complicated
that this. Lets look at that stone wall which
the door is inset within. We are only seeing about
1/3 of that surface's total width. Thus its texture
needs to be 1920x240 if we were to use a single
texture to cover the whole thing. But instead
of dealing with such a large texture, I used a
256x256 texture which is repeated four times horizontally.
If we are never going to have the entire wall
in frame at once, the repeats will be much less
noticeable.
Hope
this all made sense... :)