one-handed sword Be quicker. A shield has to be used actively. It does not give you a magical defense. If you do not know how to use a shield you are better off in a fight without it. Move in slowly and just smack his head. It sometimes startles even experienced opponents. Grab his shield with one hand and open it. Alternatively going for the head only to let your sword glide down the side of the shield to get the legs is one of my favorite maneuvers. As for "an opponent worth his salt" I manage this against my trainer, a fighter with 20+ years experience about 10% of the time. Getting lucky is always an option.
one-handed sword and ax This is one of the few sensible dual-wielding setups. Why? The ax hooks open the shield and you thrust into the opening. You will usually win the tug of war as your opponent gets slightly startled and you got Archimedes on your side. Though this is much easier against handheld shields than against those bound to the arm.
one-handed sword and shield Now you got the same setup as your opponent. The options from the one-handed section still apply. Other options like using your shield to block the enemy's sword between the shields or between your armor and shield are now available. A friend once even showed me a technique where you either give up the sword or your arm gets broken. Actively using the shield is also an option. Either straight into the face to inflict damage, against the enemy shield to open it or as a feint. Bonus point for style if you throw away your sword, in the end, bashing him to death with the side of the shield. It's way bloodier.
two-handed sword (longsword) Firstly everything from the one-handed sword applies. Secondly, the ground rule for dealing with two-handed weapons as a lone shieldbearer (battle-line is way different and beyond the scope of the question) is to run them down. The long weapon will have more range, mobility (due to the greater leverage two hand offer) and deal more damage. Thus you "untersschreitest die Mensur", the fancy German way for saying you must move into a distance the enemy weapon is no longer effective and you can bash the crap out of the enemy. They of course know this and will attempt to retreat and kill you while running backward. It is quite effective and usually, the shield-bearer wins, but not always. If the long weapon-user has a backup short-sword or dagger, giving up the long weapon for it can also be very effective. this is true for all the following long weapons.
spear High-Low, Low-High is the doctrine. Go for the face and then for the feet. Your spear is faster because of leverage. If he does not rush you, you will eventually find a gap.
Dane-axe See spear. Additionally, you can split the shield. This happens even with blunt Dane axes so a sharp one will be even more efficient. Hooking is also an option. Open up the shield, thrust the blunt tip of the axe into his face and kill him while he recovers. Or hook his knee and throw him down.
polearm See Dane-axe. Polearms are the best weapons there are. Hence their popularity in the middle-ages.
spear and shield Useful combo. You sacrifice the leverage of the spear for a lot of protection. This was the setup of most classical armies for a reason.
axe and shield The lone one-handed axe sucks for defense but is amazing for offensive maneuvers. The shield... Well, it is a simple and dangerous combination and will help you deal with the shield-bearer easily.
full plate armor I am gonna get medieval on your arse. This is not quite medieval, but renaissance. Get a set of full plate armor, laugh about how he fails to injure you, grab his shield and sword, give him a headbutt and kill him. Should you doubt the effectiveness of full plate armor, google half-swording a set of sword techniques which was developed as a response to it.
dagger You are screwed. This is only slightly better than bringing a knife to a gunfight. A dagger should only ever be your last backup weapon.
incendiary grenade Throw a Greek fire grenade at him or dirt or stones. Distract him with some sort of projectile and then land your blow, while he is distracted. Works very well.
javelin The Romans used special javelins (pilum) which got stuck in their enemy's shields to weigh them down and force the enemy to drop them. From Ryan_L's comment: "The pilum did not just weigh down the shield, it also got in the way. The lead arrowhead would bend under the weight of the shaft, leading to the shaft hanging below the shield. It would thus get caught up on the terrain if you did not hold the shield quite high. So you could either put up with your shield constantly getting stuck on things, or drop it entirely; neither prospect is very appealing."
EDIT1:
- one-handed axes, maces and mauls All of these weapons have the same fundamental problem. Amazing offensive capabilities, but due to the fact that they are top heavy they suck at defending. A shield remedies this as I already pointed out, but if you wield them alone your opponent can just parry an attack and then he grabs your weapon and a force struggle ensues. Grappling techniques are really amazing if you have a free hand. Axes are especially woundable as you can just pull the sword up the shaft and hook into the axe-head. Generally these weapons are inferior to swords as they are slower.
one-handed axes, maces and mauls All of these weapons have the same fundamental problem. Amazing offensive capabilities, but due to the fact that they are top heavy they suck at defending. A shield remedies this as I already pointed out, but if you wield them alone your opponent can just parry an attack and then he grabs your weapon and a force struggle ensues. Grappling techniques are really amazing if you have a free hand. Axes are especially woundable as you can just pull the sword up the shaft and hook into the axe-head. Generally these weapons are inferior to swords as they are slower.
