I know that you gain "relentless force" from the caverns at the beginning, and the "whirlwind" at the Greybeards, so do you always have to go into a cave to get them? If so, how do you know what caves have the dragon words in them? Are there any signs that show?

You just find them while you're exploring. I've found a few just by going in random caves and ruins.

Some are in caves, some are in the outside wilderness, some are outside of ruins, and some are at mounts (where you'll have to deal with certain somethings while you're there).

Sometimes while you walk around exploring, you might see a dragon flying around in the skies. Follow it, but be careful not to engage in battle too soon. You should soon get to a platform/ruins/mountain where in the most cases there'll be another shout inscribed in some wall nearby.
At least that worked for me once!

They can be found on Word Walls around the world. I think they're marked with a dragon head on the compass.

Be warned, there's tough enemies defending them. I've only found one, and a Krosis was guarding it.

If you go to the greybeards and ask them where to find more shouts, they will mark them on your map

some are marked with a dragons head, others are in dungeons, just go explore, do quests, kill dragons. you'll find plenty soon enough.

but do be careful, like adebar said most have tough enemies gaurding them. one was a real pain, had just killed a dragon so was heading towards the wall. freaking krosis popped out of no where. not fun. lol

Yeah Krosis was a [censored] to kill. had to advert to rock climbing and archery while using my height advantage to avoid the fireballs. But The mask you get is awesome and the shout you get is ver useful if your are a thief or assassin type.... which im not on this go around. but second go around i will be