Logic's Guitar amp is called Guitar Amp Pro. Some people prefer the 3rd party plug-in called 'Guitar Rig'... but me, well, I think with a bit of tweaking (just like a real amp) you can get some very decent and useable sounds indeed from Guitar Amp Pro (GAP).
It's not covered in any detail in the 101, ES2 or 204 tutorials, they either deal with the Core concepts of Logic or specific Instruments respectively.
I would recommend hooking up your guitar, record enable the audio track, and insert the GAP plug-in on that Channel.
Try out the presets. There are some useful ones depending on the type of tone you are after.
One important point. If you mic up an amp and record into Logic, that track will always have that effect on it.
If you record your guitar dry direct into Logic and use software effects, Logic will always record the dry sound of the guitar. This means you can tweak or completely change the effect plug-ins on the recorded audio later!
At the end of the day, if you have found the perfect sound from your analog amp then do record it that way, but if you want more flexibility check out GAP and use Logic's plug-ins.
One other trick to do with finding the right sound is to use more than one plug-in. Just like in the analog world we would connect a guitar to compressor to flanger to etc etc, you can do the same in Logic, and you can easily change the order of the plug-ins too :)
OK. This is becoming a very long post, sorry! There is one tutorial called Logic's Plug-ins Unplugged:
It is brilliant, and it covers GAP in video 23.
Now, the disclaimer ;)... This video was created for Logic 7's plug-ins. Now one of the biggest changes between L7 and L8 is the interface. That applies for plug-ins too. IMHO the majority of plug-ins look the same/very similar. There are some, e.g. Multipressor that are quite different. Luckily, GAP looks and functions the same.
To learn how the plug-ins work and how to use them this tutorial is a mine of information.