The manufacturers who make the kind of keyboard you have do not intend for them to be replaced, so it is much more difficult than it needs to be to replace one. Essentially you have to melt or cut off the plastic welds holding it in place, then secure each pin, whether that is by re-melting them, using some sort of glue or even hot melt glue. Although it's not specific to your laptop, here's an example of replacing a keyboard that's held together like yours.
SOLVED: How do I replace the keyboard? - toshiba satellite c55-c5241 - iFixit
The question and answer doesn't really have a guide as such, but does have a link to an instructional video that will give you the basic idea of what you will have to do.
Toshiba Satellite C55-C keyboard replacement - YouTube
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