Accessing hidden folders from Finder
If you need to go to a system folder not visible through the "normal" Finder, do the following.
Once you have the Finder dialog open, press
Cmd+G. Here, enter the path to the folder you want to open.
Accessing hidden files or folders from a dialog
You can show hidden files from any file open dialog by pressing
Cmd+Shift+.. Thanks to @kine for mentioning.
If you want to always display hidden files (those starting with a dot or hidden through the extended file attributes), enter the following in a Terminal:
defaults write com.apple.finder AppleShowAllFiles TRUE
Then, reload the Finder by
option-clicking its icon and selecting "Relaunch".
You can also toggle this option more easily with an AppleScript. See this post for instructions on how to save the AppleScript as an application that you can use to toggle the option without having to use a terminal.
Directly opening system files through the Terminal
As per Andrew's comment above, of course you can just enter the following:
open -a TextEdit /etc/hosts
open -a TextEdit ~/.somehiddenfile
Or, even shorter:
open -t /etc/hosts
-t Causes the file to be opened with the default text editor, as determined via LaunchServices