Wall of Likely Useless Information Incoming!!
I would not (or ever) call myself an expert on Pokémon, but I would like to bring some points up that may or may not be helpful. Either way, I'll go ahead and try.
So first of all, you must have a varied team to cover for type advantages. These are the 'fire is weak to water' scenarios, except there are 17 or so different types, all of which have multiple advantages and disadvantages (Note: the exact number of types will vary based on which game you play. If you play a generation 1 game (that is, Pokémon Red/Blue/Yellow, you'll only have 15), if you play a generation 2-5 game (that is, any Pokémon game on the Gameboy Colour all the way to Nintendo DS (BUT NOT 3DS), then you'll have 17 different types which the addition of Dark and Steel. Generation 6 (3DS) has 18, with the addition of Fairy. Note that new types are added in an attempt to factor out against previously-too powerful types (more on this later!!).
Super effective = x2 damage
Not very effective = 1/2 damage
You're advised to look up a type advantage/disadvantage chart and study the general effects. Of course, you'll be able to get the information from the game itself, but it requires perception and memorization (for example, you hit a Pokémon with an attack - is it super effective? Is it not?). The latter would be nice if you were a purist who would like to have a bit more challenge, but someone such as me would not have the patience.
Second, you must know your own Pokémon to some degree. Of course, you're likely aware your Charmeleon is a Fire type, no? Like mentioned above, factor in type advantages and disadvantages. Besides that, make sure to check out your Pokémon's statistics (Menu > Pokémon > Pokémon of choice > Summary > press left or right to go to right section) and see where their strengths and weaknesses are. For example, your Charmeleon would probably have high Speed and Special Attack statistics, so you may base your moveset around hard-hitting attacks backed by speed.
Also, you should know that if a move's type is the same as the Pokémon's (Ember and Charmeleon are both Fire), then there will be a x1.5 power boost. Of course, if taking into account Pokémon types, it'd mean your Pokémon would be able to do x3 damage as opposed to x2 (or 3/4 damage as opposed to 1/2).
However. Although you'd be tempted to use a moveset that consists entirely of Fire attacks, that would likely be a mistake. Instead, you'd try to add different move types to a single Pokémon, in order to factor out against any weakness. For example, you likely have Metal Claw. If you haven't beaten the first Gym yet, Metal Claw will do your Charmander wonders! Why? Fire is weak against Rock, but Rock is weak against Steel type, meaning that your Fire type could overpower the first Gym with ease, probably. You're advised to take this general idea and take it further: see if you can add moves that'd be of use to you. Discard moves that are of no use to you.
(Wait!! You likely DON'T have metal claw -- that's only in the FireRed remake... >.<)
This also works for your entire team in general - get varying Pokémon which all factor out for others's weaknesses, such as getting a Grass type to cover for your Fire type.
By the way, now I mentioned the first Gym, you'd better prepare yourself for the second Gym - water-based. There, your Charmeleon will simply not cut it unless your Level is ridiculously high by that point. You'd have to catch a different Pokémon to work with for the time being (or just overlevel as hell).
To end things off, I'd like to bring up a point. Remember how I previously mentioned that some Types are a bit overpowered? Well, if you're playing Generation 1, for example, try getting a Psychic type such as Abra, which will evolve into an Alakazam. Why? Like mentioned before, if you're playing a Generation 1 game, it will become REALLY powerful! And no overestimation either. You see, in Generation 1 Psychics only had two weaknesses - Ghost and Bug. Now, due to a glitch in the game, Ghosts, instead of being super effective, did x0 damage. Ouch. As for Bug? Well, there were no Bug typed attacks powerful enough to pose a threat (the strongest of all being the same as your measly starter attack, Scratch).
But wait, now I mentioned Alakazam... you usually cannot get it on your own, because you are required to trade over Kadabra at least once to make it evolve into its final stage. However, if you're playing on an Emulator, you can rectify this problem by... erm... (wait, you'll likely have to transfer your save to a computer and trade there and then transfer back... likely).
So... with that brought up, you're not advised to work with a Bug type... at least, not if you're playing an early Generation game.
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Er... I'm wondering whether you could even comprehend any of this... I think I got a bit carried away. B-but still, it's not complicated business, and the learning curve is not very harsh. Keep in mind that the games are designed for children, so if you just kept yourself to leveling up and overpowering all your foes through brute force, then by all means.
Some more basic things: have a ready supply of healing items, such as Potions and condition-healers (oh boy, haven't mentioned those yet. Let me go on a 5,000 word rant about them, too! (jk)). Also, have a good supply of Pokéballs if you're planning to catch something on the way.
Conditions are... well, what the names say: conditions. Usually, there is a school-like building early on in the game (I know there is one in Viridan City) that talks about conditions, so rather than me talking about them, you can go on and visit that.
Also, someone above mentioned that fighting 'random wild Pokémon' is a good strategy for leveling up. It is the most basic, yes, but it can also be time consuming. Trainer Pokémon are often quite a few levels stronger, and have a x1.5 experience gain boost on top of that, meaning they are much better for leveling up. However, they are in limited quantities, and will run out (in Gen 1, that is). Fighting Wild Pokémon, on the other hand, is slower, but it will always be there.
......Erm... now I really think about it... I'd advise you to switch over to FireRed, the Gameboy Advance remake of Pokémon Red. It's a bit... HEAPS better than Pokémon Red. In my opinion. Pokémon Red is fine, but it is awfully dated. It is also inbalanced and diffucult at times, but not due to the right reasons. If you insist on playing the original, would you be interested in at least a small graphical update? (for example, you are likely aware of how pixely your Pokémon look like from the back, right...?) If interested, PM me. If not, ignore me then.
Okay, done!!
Anyhow, I think that covers everything I wanted to say. I doubt it was any useful. But hey, you can always ask if you need something clarified. I still stay by my claim that you should switch over to Pokémon FireRed for a generally better experience, but if you say no, then okay. If so, I still stand by my claim that you should contact me about that small graphical mod (which alters the Pokémon's battle sprites), which should work with no problem on your emulator, and which I have readily available if you ask. If you're wondering, it looks like this:
However, you're still going to play in fully black and white, or whatever colour scheme you have on your emulator. Why? Because for colour, you need to set your emulator settings to something specific, and as far as I know, no Phone emulator has access to these settings.
Edit:
Below me, someone mentioned you should catch a Pikachu in Viridian Forest - I agree. Go for it! It'll do you a lot of good when fighting the second Gym! However, depending on your luck, it might be take ten minutes... or a few hours. For me, it was the latter... As such, I made sure the catch did not go to waste (see below).
Oh yeah, your hidden message - it's a pain to read, so I waited for someone else to do it. Thanks, Kelpie.
Anyhow, now you made this thread, I suddenly have this urge to finish off my FireRed playthough... And now I think about it, I still have the playthrough. I wonder how I was doing... Whelps, the big reveal that I'm terrible at keeping a balanced team. Also, those are some amazing nicknames I got there. 'McSPARKY', 'KAKAROT'... Mhmh... Everyone is either horribly useless (still hoping to rectify that) by this point or just flat out too useful, making the game a cakewalk (that is, until the Elite Four, where even the too-useful won't cut it... (Oh wait, they just did. I guess I was wrong yet again...)