This list will show my process to finding a solution if there is one.

1.) Search engine. Common search terms you should try are;
(game) turn off filter
(game) nearest texture filter
(game) point sampling
(game) commands
If you find yourself on a commands list page, search for common phrases such as;
filter
linear
smooth
aniso
mipmap
point
If you still can't find it, it might still be there but just not under this umbrella like Mednafen with videoip.

2.) Scan the config files. These are often located, from most to least common;
the game's folder
~/.config, ~/.local/share or just ~ (these are hidden files and you will have to show them with ctrl+h) for *nix
AppData folder (%APPDATA%) in Windows
My Documents folder
registry
your user folder (above your My Documents folder, assholes put shit here!!! looking at you super tux you piece of shit)
Common extensions for config files are .ini and .cfg, and the files themselves are normally named User.ini or Config.ini or something else to that nature. You would open these extensions with any text editor of your choice, such as notepad in Windows. Scan through them the same as you would a commands list, with the previously mentioned umbrella terms, and since the options are normally true/false or 1/0 you could just flip off the filters (if this is an option).
I would like to mention the Unreal Tournament solution for turning off texture filters. The solution itself was not under the correct renderer (Direct3D/OpenGL), but only located under the Software renderer.

3.) Autocomplete in consoles.
Some games have autocompletion on as you type (Source engine games) and you can tab complete to cycle through all commands with what you have already typed that are found in other commands, and some require special arguments like for example, you can only tab complete commands in Quake I if \ precedes it. Yes \, not /. Some don't even have that, but what most games do have are categories. Options for texture filtering will often be located under a video category, usually determined by a prefix. Again to reference these, in Source games, video options will be prefixed with mat_, and in id Software games they will commonly be prefixed with /r_ or later /cg_. Oftentimes texture filtering arguments will be found prefixed with gl_ such is the case with the id Tech 2 engine. The point is though, if an autocomplete option is present you will often be able to cycle through the list of commands starting with whatever letter you choose by repeatedly tapping the tab key, so you would be able to find the command without even knowing what to start with if it exists.

4.) Try software renderer if available (which could end up being a solution to the resourceful(see again the Unreal Tournament page)). An unfortunate end, not really worth doing as then you would have shitty fps and I personally prioritize gameplay over looks.