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My 3D modeling skills are limited to SketchUp, so forgive my lack of experience. I don't understand how to model something, in programs like Blender, with precision when it comes to measurements. How can I make something exactly 1/4 inches thick, or extrude a face by 2.38 inches, or 25 mm?

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You can just enter an amount when some operator is called.

First you'll have to set your units:

enter image description here

Then, if you choose Metric, you can press, for instance, E (Extrude), and then press, for instance 2, to extrude the selected vertices, and move then by 2 meters.

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    $\begingroup$ That is exactly right! Very handy feature in Blender! Note that in orthographic view you can pres Num + 1, 3, or 7 to get the different angles, with a grid to help free-hand drawing and modelling to scale. $\endgroup$
    – VRM
    Nov 25 '14 at 19:07
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    $\begingroup$ You can also type eg 2cm, 2mm, 2km in many boxes instead of using decimals. Doesn't seem to work in the "transient header input" modes like during an extrude, sadly. $\endgroup$
    – StarWeaver
    Nov 25 '14 at 19:30
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    $\begingroup$ @StarWeaver, works during transform here (2.72 release) $\endgroup$
    – ideasman42
    Nov 25 '14 at 21:46

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