You want to turn a game that had no SRAM type save (presumably/hopefully a password save though) into one with one? The alternative is some kind of SRAM launched cheat/hack which has been seen many times (usually for hacking the console itself but hey).
For the NES it is a bit more annoying than some later systems but anyway there are 3 main options
1) It was there in beta/development but disabled for the final release. You then enable it again.
2) It was there in another region. Same deal really except it might be easier to backport the translation instead.
3) You actually hack the game, this takes various forms.
The reason I said presumably/hopefully it has a password save system is because that makes things considerably easier. In those cases you will probably want to just figure out where the game stores the data behind the password when it displays it to you when you quit/end a level/whatever, put that into SRAM and (as it will likely be the same as the data used by the password entry screen) then fetch said data from SRAM and put it into the decode point for the password restore screen. If you are really good then you can also store things the password might lose; I usually use the example of Road Rash on the megadrive/genesis that will store you bike, money and progress but not your current weapon (they are easy enough to get in a race but there are some desirable ones that might not be in a given race or benefit you to have earlier in the race, whether this was an intended effect I will leave for another discussion).
If the password is not a binary storage mechanism ( http://tasvideos.org/PasswordGenerators.html
) and instead some kind of glorified level select ( http://uk.ign.com/cheats/games/worms-2-pc-3143
) then it might be even easier.
The biggest trick for the NES will probably involve mappers (and on cart chips for the SNES or possibly memory bank controllers/mbcs for the GB/GBC) as such things often do on the NES and such things will vary -- if there is not one there then you are going to want the mapper setup to gain itself a SRAM bank (or sacrifice an existing bank to become one), and then you are going to have to do the bank handling/restore. Something like the GBA on the other hand has SRAM (or EEPROM or Flash) mapped directly in memory and beyond having to observe access protocols, wait periods and read lengths (all simple enough as far as such things go) it is nothing pressing at all and if the emulator or flash cart handling program supports the save type (you would be hard pressed to be troubled here) then you are good to go.
Redoing all the menus would make this a far longer hack so if you want to leave the password display and restore functionality mostly intact then it is not going to hurt anybody, give or take people maybe overwriting a save if they are not careful.
The other type of one is for when a game has no save at all and not so much as a password system. Not as common on the NES for games that would really benefit from it as it was on the older consoles (see also the jokes/comments with people leaving the console on over night/over dinner/over the school day...) but far from unheard of as well. Not a fun thing to do if you can help it but not impossible either, just long.
Two approaches here.
1) A savestate is the ultimate form of this but doing that in hardware, especially without extra hardware like a good flash cart or debugging board, is hard, even if you somehow have one of those save game chips that is comparable to the amount of memory a given system has.
You work backwards from this chopping out things you do not need.
2) You make a save. Kind of the reverse approach from above -- where you would trim a savestate for the above here you would figure out what the game/player needs and implement a full save encode and decode function. So you reckon level progress, score, maybe some upgrades....
For some games this might be trivial as they have no score/lives/whatever and you can just trigger a branch that ends up starting level 4 or whatever, for others it is going to be a nightmare as you figure out what is needed.
In both cases you are probably going to have to map the memory out and figure out what it what. For the password based stuff you might well never even have to know what the password is composed of as far as data, checksums and whatever else.
I do not have an example of this second kind of hack to hand. The vast majority will be unlocked functionality from dev/beta or another region, or it will be some kind of password system based hack. Likewise it is probably no coincidence that a game series as well hacked/disassembled/understood as home console megaman was picked.
I have a feeling I trailed off somewhere in there and forgot something important but I have to go do something so I will leave it there.