This is not meant to comprehensively cover every Bear Power in the game—we'd like to think that we did a reasonable job explaining some of the Bear Powers in the in-game text. But we also know that sometimes we didn't do that great a job explaining all the nuances of a particular Bear Power, so we'll try to do that here.
Break Rock Tile
To use this power, first tap the power's icon at the top of the screen. An overlay will appear in which the rocks are highlighted and everything else on the board is not. Tap any rock on the board. The rock you tapped will turn into a bear, and one usage of the power will be consumed.
If there are no rocks on the board, tapping the power icon will still bring up the overlay. But there won't be any rocks to tap, so you'll have to cancel out of the overlay screen without using the power. (No rocks is a good thing, though! And you'll conserve your usage of the power for when a rock does appear.)
When you activate this power, the game goes through the letter tiles visible on the board. For each letter tile that is not already A, E, H, I, N, O, R, S, or T (letters that we decided are "simpler" to use), the game tries to randomly make it one of these letters. There is a small chance that some letters won't be so converted.
Note that this power only applies to letters that are already visible; a letter tile that has not yet been revealed will be unaffected by this power.
Summon ING (or some other combination of letters)
To use this power, first tap the power's icon at the top of the screen. An overlay will appear in which letter tiles will be highlighted if the power can be used on that letter tile (more on this in the next paragraph). Tap one of the highlighted letter tiles and the game will try to spawn one each of the letters I, N, and G into empty squares immediately neighboring (including diagonals) the tapped letter tile.
The valid spaces where the summoned letters can spawn are the empty squares that are immediate neighbors (including diagonals) of the letter tile you tap. If there are fewer such squares than letters being summoned, not all of the summoned letters will spawn. If a letter tile has 0 such squares around it, that letter tile won't even be highlighted since nothing can be summoned around it. If there are no highlighted letters, you'll have to cancel the power usage and perhaps try again later.