As the tank was a new thing in WW1 most of the tactics were improvised, the simplest being simply pointing an artillery peice at the tank and direct firing on it. Late in the game the Germans for sure and I would guess some of the other players developed some early anti-tank rifles. I would imagine that the tactics of jamming the treads to immobilize it, simply getting close enough to fire into the viewports, or dropping a grenade down the hatch were first tried at that time. As for WW2, the anti-tank rifle and gun concept had been developed further though the panzerschreck and panzerfaust proved more effective than the AT rifle. Also, the Finns developed the innovative tactic of the Molotov cocktail during the Winter War of late '39 to '40, get around behind it, and through the cocktail onto the engine's air intake. The burning gas gets sucked in and you've destroyed the tank, either catastrophically or simply to the point that its engine is just hashed. Even then it makes it easier as what makes the tank so lethal is how difficult it is to destroy as well as being mobile, take away the mobility and its little more than a fixed fortification that is much easier to deal with. Satchel charges and mines are another method that was also used. IIRC it was also during WW2 that the concept of the best anti-tank weapon being another tank was developed. Today I'm not sure, though I know that the Molotov is not too effective as there have been countermeasures developed to keep flames from being sucked into the intake. Also, armor has been developed from simple steel plate to a composite of materials that is incredibly stout. Rather than explosive charges anti-tank rounds fired by the most modern tank guns today are sabotted rounds down a smooth bore and its basically a lance of hard material (depleted uranium usually IIRC), shaped and travelling at such velocity that on impact it peirces the hull and sprays a jet of molten metal inside with catastrophic results for the target.

When it comes to destroying tanks, it matters a lot whether you're on the offense or defense. The best defense against tanks was artillery during both world wars. If you were the Axis during WWII you especially did not want to get your tanks within range of the battleships sitting off the coast during an allied landing. After they got through with your tanks you wouldn't have much left. If you're on the offensive, it's a little trickier. You don't necessarily know where the tanks are to blow them up with artillery and sometimes you're just too close. So, many methods were used, best described in the previous question. If you're on the offensive in this day and age, it's all about air power. Bombers can take out pretty much any vehicle on the ground with a variety of missiles. If you're on the defensive nowadays, and the enemy has total air superiority, you use stay in the city where their usefulness is limited and they're much more vulnerable. (Terrain can be an anti-tank defense.)