This is something I do a lot, so I figured I'd write up some of the things I've learned that help speed things along.
What is Smeargle Breeding? Smeargle Breeding is using a male Smeargle to pass on moves that may otherwise be difficult to pass. For example one time TMs, or moveset combinations that are impossible to breed otherwise. It may also be worth considering if the conventional breeding chain for the moves you are intending to pass along goes several pokemon deep.
*This assumes you are already familiar with regular breeding and breeding chains. If not, you may want to read up on that before continuing. Here are a few links: [legendary pokemon], [bulbapedia], [serebii] (there are plenty of other good resources as well).
Why Smeargle? Smeargle can learn any combination of moves imaginable (with a few exceptions such as Transform). Once he's learned these moves, a male Smeargle can pass them on, just as any male could. Thus you can have him learn virtually any moveset of egg moves and TMs you would like to pass along.
What's the Catch? Smeargle is in the Field egg group (also sometimes called Ground). The Pokemon you want to learn the moveset must also be in this group, or have a breeding chain that leads to Field. This is usually not an issue for passing on single moves. This may be tougher for passing multiple moves, since each pokemon in the chain will have to have all the moves in the intended moveset as an egg move or learnable TM. This does limit the usefulness of Smeargle breeding, but it is another option to consider when regular breeding chains won't get the job done.
Give me an example. Say hypothetically Ranger Steve calls me up, and the topic of giving a Lapras the move Avalanche comes up. I let Steve know that his options are 1) use his Avalanche TM, or 2) Smeargle Breeding. Conventional breeding will not work, since the only Pokemon that can learn Avalanche, Jynx, is always female, and thus cannot pass along the move. Steve can use his TM, and then reset and play through the game again if he ever needs another one, or have Smeargle learn Avalanche from Jynx, breed Smeargle with a Delibird, then breed a male child Delibird with a female Lapras, thus keeping his TM for a Pokemon that Smeargle Breeding will not work for.
Will Smeargle Breeding work for me? If the pokemon you want to pass moves to is in the Field egg group, then the answer is always yes. You will not need to chain, so you can pass up to four egg moves or TMs with little difficulty. If this is not the case, you will need to make sure there is a breeding chain for the moves you want to pass. This is pretty easy for one move, but the more moves you have planned, the harder they will be to chain. I find
this search tool to be very useful. To start, I suggest adding Field egg group to the search, and add each move you wish to pass (check the TM and Egg option, but not the level). This will let you know if there is a simple chain (one intermediary Pokemon). If one of the resulting dual egg group Pokemon shares an Egg group with the Pokemon you wish to ultimately learn the moves, then this will be your "bridge" Pokemon. If not, remove the Field egg group condition, and see if there is a chain with the resulting Pokemon listed. When doing either, remember you will have to ignore any Pokemon that isn't the first stage of its evolution. If a Pokemon can use a TM after it evolves, but not in its first stage, it will be no use in breeding chains. Also remember to ignore Pokemon that only come in one gender (or no gender). Your end result Pokemon can be female only, but everything in the chain must come in both genders.
What do I need? You will of course need a male Smeargle. They can be caught on Rt. 212 with a PokeRadar, or Pal Parked over from a GBA version of the game. You will need to have a Pokemon that knows the move you are trying to pass on (in the case of multiple moves, the moves can be spread over multiple Pokemon). You will need a female of the pokemon you wish to learn the move(s). You may also need other female pokemon depending on whether or not you need to chain breed. Heart Scales may be needed if you need to have your Smeargle relearn sketch and you can't/don't want to level up to learn it again. The Vs. Seeker is also very helpful.
How do I get Smeargle to learn the moves I want? Sketch works by permanently learning the last move it's target used. This can be tough to time or even survive against an opponent. The easy way to ensure success is to use it on your partner in a doubles battle. Have Smeargle and a pokemon that knows the move you want to learn be in the first two slots in your party, so they both come out in a doubles battle. Then find yourself some doubles opponents. I generally use the father / daughter pair just north of Solaceon Town, since its close to where I'll be breeding anyway. Use the Vs Seeker to get them ready to fight. If your Smeargle has a lower Speed than your other pokemon (the best case), have your other pokemon use the move you want to learn (it doesn't matter who is targeted), then have the Smeargle use sketch on your other pokemon. As long as Smeargle survives until its turn, the move will be learned. If the Smeargle happens to be faster, have it use another move (either killing an opponent, or protecting is preferable) while your other pokemon uses the move you want to learn. Then have Smeargle use sketch on your other pokemon second turn. Once this move is learned you can heal up, learn sketch again via leveling or heart scale, then repeat for the next move you want to learn (if any).
Got the moves I want on my Smeargle. Now what? Now you get to breedin'! Take that Smeargle to the Day Care Center. If you don't need a breeding chain, then give them the female of the Pokemon you want to learn the move, and wait for your results. If you do need to chain, give them a female of the first Pokemon in your chain, and wait for a male child. Retrieve the parents, then enter the male child and a female of the next pokemon in the chain (you may first need to evolve the child if it is a pre-evolution such as pichu or cleffa, make sure not to lose those bred moves). Repeat this down the chain until you get to your end result pokemon.
So there you have it. Sometimes it's quick and painless, sometimes it takes a bit of work. But it's an option to consider if you're hesitant to use that TM you got from a Gym Leader, or can't seem to chain a specific moveset through normal means.
