Finding all placements in a grid for certain polyomino

How would I find all possible placements of a certain polyomino within a grid? For example,
just looking at the T tetromino without transformations (excuse the MS paint skills): What is the fastest way to figure out how many ways I can place that tetromino on the just a rectangular grid like the first grid? Would there have to be a different method for irregular grids like Grid 2? Is the only way to brute force it by just placing it on every cell and seeing if all of the tetromino is within bounds?