If your trying to put Braille on to a keyboard, don't bother. A student can learn to touch type without having a tactile representation of every key on the keyboard. Using typing software that echoes the keys pressed is really all that is necessary.

There are 64 (or 256 symbols for 8 dot) patterns or symbols but they don't map to individual keyboard keys. The meaning of the dots, at least for Latin languages, is contextual. There are symbols that indicate numbers, capitalization and special special symbols and contractions. These symbols would be followed by other characters completing a more complex symbol. The most common runs of simple characters where one pattern means one symbol would either be the lower case alphabet or number digits. Possibly what you are looking for though is Braille to English transliteration tables which would decode the braille coding in to standard English text. The process is transliteration rather than translation, though it is often commonly called translation, as Braille is a writing system, not a different language.

You mean, including things like semi-colon and question mark and such?

https://www.teachingvisuallyimpaired.com/uploads/1/4/1/2/14122361/ueb_braille_chart.pdf

Not sure if this has everything.

So, there are several aspects to your question, some techy, others not. I'll cover the simple ones first:

Every braille language has a list of their most used characters. Usually available if you look at Wikipedia "<language> braille", aka Japanese braille. In addition, associations for the blind often offer braille alphabets.

Now to the techy part:
If you talk about braille keyboard equivalents of e.g. modifier keys, then this hugely depends on the operation system used, the device (braille display) we're talking about and any user-specific settings.

For iOS, there are the following modifier key combinations:
Command on/off: space plus dots 1 8
option on/off: space plus dots 2 8
control on/off: space plus dojs 3 8
Caps lock (shift) on/off: space plus dots 4 8
Function on/off: space plus dots 5 8

This is useful if a web site has key shortcuts (e.g. WordPress editor) or to use Mac accessibility key combinations, like control+option+command+c to copy last spoken text to clipboard (equivalent of four times tap with 3 fingers).

On Windows, Apple OS (and probably Linux, too?) you can additionally assign your own key combinations (braille or otherwise) to trigger scripts or key actions respectively.