I have a couple of tattoos, but I'd like a partial sleeve. Maybe a half-sleeve or quarter-sleeve on my upper arm. 
How long does it take to get a half-sleeve done?
Well, there's a difference between an arm covered in tattoos and a sleeve tattoo. A sleeve has a unified theme and may take many sessions to complete. 
How painful is it? I have never gotten one.
Certain parts of the arm hurt more than others, the inner arm and elbow areas for instance. The pain comes from using needles to insert dyes and pigments into the skin. 
Do the colors in the tattoo fade over time? I seem to always see people with faded and dull tattoos.
They do, especially with sun exposure. After the initial injection, the pigment disperses down through the dermis layer of the skin to become permanent. 
How do you find a tattoo artist? I would be afraid of just picking someone at random.
It's best to ask someone with tattoos you like who did them. The tattoo artists typically learn through an apprenticeship under an experienced tattoo artist. 
That seems wise. Do you worry about the stigma of tattoos?