I'm bored on standby, so here's what I have - You'll see a lot of "typically" and "usually" because no generalizations are ever 100% true. (Disclaimer for the people who say "you must be 20nm away at all times": I never fly through or really close to a thunderstorm if I can avoid it. I never put myself in a situation in where there is no way out, and I'll land before I endanger myself. Realize there are situations where I can safely go in a freight airplane that would not be safe for a pax operation simply because I don't have to worry about "the ride" or people standing in the aisles. Cargo don't complain, after all.)
Preflight: This is very important, it gives you the 'big picture'
Take a look at the radar,
Where are the tops? Above FL300 has a much greater chance of being a severe storm.
Are the gaps closing or opening? If closing, are there ways around the whole system, or can you stop on the ground and wait for it to blow over?
Are there a bunch of "pop-up" storms that fade away almost as quickly as they arrive? Typically this is easy to fly around.
Is there a line? If yes, are there gaps in the line, how big are they, and are they opening or closing? Southern cells in a line are typically more severe, avoid those.
What is the history of the storm, is it in the building or dissipating stage? If it's raining itself out (becoming a weaker echo, with lower tops) it's usually much smoother to fly through, and may be gone before you get there.
Which way do you go if it gets bad?
Check pireps, tafs, lifted/k, etc. for an idea of what the forecasters think will happen. Realize who's giving the pirep. Freight dog saying "moderate turbulence?" It'll be bumpy.
Where are the fronts, where is the whole system moving?
If you can top the storm or stay below the bases, you've got a great chance at getting through. Ask any pilots you know who came from that direction. In flight you can also query ATC to see if anyone has been through where you're going.
Approaching a storm:
Ask ATC what they see, and/or if there's a way around.
How does it look? Dark and foreboding? Lots of vertical development? Very dark rain shaft? Very frequent lightning strikes? - Bad news
Look at the radar if you have it.
Can you paint the ground behind the storm? If yes, it probably isn't too bad.
Does the storm have a very steep gradient (green-yellow-red spaced very close together?) and does it boomerang towards you? - Bad news, go somewhere else. Very oddly-shaped storms are also usually more severe.
(As an aside when you're painting the ground make sure you don't see a lake or ocean and assume it's a "shadow," bodies of water show up as black on the screen.)
Use your eyes. Flying towards the lighter spots will usually be safer and a smoother ride. If you can stay below the cloud deck and avoid heavy rain shafts, you can pick your way through almost anything with very few bumps.
If you get caught in a storm
SLOW DOWN to turbulence penetration speed prior to the storm if it looks at all like you might be in for a ride. Tighten your seat belt, keep the attitude level, and don't worry about altitude deviations if it's really bad - ask for a block. Don't turn around, it's usually quicker to go straight ahead and the increased load on the aircraft from turning can get you in trouble. Keep your eyes on the instruments until the danger has passed.
Stay away from the freezing level, 15 degrees C on either side of it is safer.
Using radar:
Below 15k - take your height in AGL and divide it in two then divide by 1000 (IE 7000 agl = 3.5). Paint the ground so there's a solid line 20nm out, then tilt up by what you found above. So, if you're at -1 degree at 7000 agl, go to +2.5 degrees. This will bring the lower part of the beam level with the ground. If you see anything, tilt up and down to see if it's a storm or ground clutter.
If you're above 15k, paint the ground at double your altitude (FL350, paint the ground 70nm away). Again, use tilt to identify what you're painting. A shadow is when a storm is so strong it absorbs all radar energy, you'll see a steep gradient followed by what looks like a hole. Don't go that way.
This is what I use when flying around weather, your mileage may vary, no warranty is expressed or implied, etc. etc. I'm sure I missed quite a few things, but I wanted to give a better insight to people who don't have weather experience. Hope it helps.