Spiders, and most invertebrates in general, communicate through touch, vibration, and pheromones. Spiders for example have bad hearing and generally bad vision so to communicate with one another on an individual web (for web building species) they sometimes pluck the strands to cause vibrations communicating with the other spider. In relation to training spiders though. I don't have any personal experience training spiders exactly but I have trained a whip scorpion and a giant centipede, both of which are my pets. They both have very similar nervous systems to that of a spider and learn in similar ways. The whip scorpion I have trained to a point of being able to do medical checkups on him on command and pick him up from above which invertebrates generally won't let you do. I am still in the process of training the centipede (I only got her about three months ago) but with working with her she has calmed down quite a bit and we have began doing handling training for education programs.

Tarantulas are sometimes kept as pets in some parts of the world. They are very large and furry of course, unlike most spiders.

I don't know how familiar they ever get though. They obviously have some pretty primal and simple nervous systems. I expect they can become familiarized to some extent.

Spiders are really dumb little nits, and don't really communicate with one another, save for a male courting a female may dance or strum on a web to identify itself.

You can become familiar with spiders, and get to know their behavior, but spiders just respond to natural instinct. They can acclimate say, to your hand they may take as a threat, but if they don't perceive a threat, they will calmly just crawl on your hand. My pet hobo spider is a bit skittish when I try to pick her up, but she quickly settles down and freely just crawls on my hands.

Grass spiders spook easy and may be quick to run, but not much different.(hobo spiders are grass spiders)

I have had more pet spiders than I remember, and handled all of them. Some are docile, some quick, and some like sac spiders just don't like hands.

As for 'training' spiders, nope, won't happen, but you can seemingly make them do tricks.

The wrangler for the movie Arachnophobia made a small huntsman spider crawl across 4 feet of floor and into a slipper without touching the spider. Amazing what they will do with certain stimuli.

A small grass spider lived on my desk lamp most of a season, but if I try to touch him, he takes off like lightning, but didn't mind my presence otherwise.