General Strategy

Of all the characters in Smash Brothers, Link is the most well rounded. He does not nearly have the speed of Fox, but he's not painfully slow like Samus, DK, and Jiggly Puff. Most of his attacks come off quickly, but recovery from some of them is quite slow. Link's highlight of course is his sword, and I find that his best moves are his quick sword slashes. These offer quick execution, and quick recovery. Up and A, and Side and A while in the air are both excellent sword moves which display both of these features. Link also has the advantage of his hookshot. This gives him a throw move with range. For beginners good strategies will be to use the hookshot (Z and A, or R), to chuck bombs everywhere (Down and B), and to use the spin attack (Up and B). These all have good range while not requiring a good deal of accuracy, however the bombs and spin attack have slow recovery time. More advanced users will want to make more use of the downthrust (Down and A while in the air), and the above mentioned swordplay moves. The downthrust has slow recovery, but this won't matter as long as you hit them because it is powerful enough to send them sailing away from you. Advanced users will still want to make use of the hookshot because it is fast and has good range.

One-on-One

Recommended method for dispatching a single opponent:

When first encountering an opponent, their damage will be at zero and they will therefore not fly very far when hit. Use this to your advantage. With Link, use his Up and A sword slash (as shown above), and continue tapping A. Your opponent will be juggled in the air and slashed repeatedly because they are unable to escape. Eventually their damage will be high enough that they will fly out of your reach, but by now they should have about 40% damage. Now that they fly farther when hit, you should also use this to your advantage. Jump over your opponent and do a downthrust.

Downthrust is a powerful move, but has a slow recovery. This won't matter as much anymore because it should knock the opponent far enough that Link will recover before he can come back and put in a move. While the opponent is still at somewhat low damage, after doing a downthrust turn and face them then use your hookshot.

If done in sequence, it should catch them off guard when they're just recovering from your downthrust. When they get to higher damage, they will be out of range of the hookshot right after being hit with a downthrust. Now jump towards them and hit Towards and A while in the air. This will make your sword spin in a quick circle, from which you will recover quickly. Continue this until they have been knocked off.

Groups

In this game there are five different group situations. Yoshi team, Mario Brothers, Kirby team, Fighting Polygon Team, and Vs. Mode. I will only explain four of these because Vs. battle should usually be treated as one-on-one since it is free for all (team battles don't happen nearly as often).

In fighting the Yoshi team there are two strategies, either of which work just as well. The first strategy is to stand on the bottom platform and wait for Yoshis to land on a platform above you. Then you jump and hit Up and B so that you come up underneath them doing a spin attack. This is the easiest method, but usually takes more time. The second strategy is to stand on the bottom platform and wait for the Yoshis to come down to you. You then quickly dispatch them with the hookshot. Be careful not to allow Yoshis on both sides of you because one will invariably turn you into an egg while you are hookshotting the other. This is easily overcome by standing on one edge or the other.

The Mario Brothers have always been difficult for me to fight, and I have never found one overall strategy that always works against them. One thing that I have found that usually works when playing on easier difficulty settings is to stand on the moving platform and wait for them to come to you. Then hookshot them off the edge as the platform is coming back in. Another strategy is to stand on the bottom platform and throw bombs up to the top platform where they are. Usually though, I just use a lot of quick sword moves because the Mario Brothers are quick and will take advantage of any time you take to recover from a move.

Kirbys are not quite so simple to beat. Because there are fewer of them they have a higher intelligence, and are slightly harder to knock off. Some of them also have guns which can be very obnoxious in a group battle. The best way to dispatch them is to wait for a decent item. While waiting for one you should stand on the bottom platform in the middle with your shield on. When one happens to wander in front of you, wait for it to attack first, then while it's recovering tap A while still holding Z so that you will hookshot it. Don't let one wander up behind you, or it will probably use its throw on you.

I find the fighting polygon team to be incredibly easy using Link. I have no trouble anymore beating them on very hard with one life. Stand on the bottom platform in the middle with your shield on. Tap A to hookshot one. If one comes up behind you, then while still holding Z hit to the Side to roll behind it. Then hookshot it. The hookshot is quick and efficient against these guys. Sometimes you will even knock off two at once when a guy you are throwing off the screen runs into another guy. Always be on the lookout for items in this round, especially hearts and tomatoes.