Well, there's a lot to MGS 1 and 2. I'll try and go through a few different...points of views? Hmm...I'll try to explain it as organized as possible.
MGS1- Liquid Snake, a clone of Big Boss, takes a special forces army, (genome army) and takes over shadow moses island, in alaska. It's soon realized that Shadow Moses is where Metal Gear is being kept, and that's Liquid's main form of bargaining. By taking control of Metal Gear, Liquid can blackmail the US...If other countries knew that US had a Metal Gear, the world's balance of power would be extremely thrown off, and also other countries would start trying to replicate their own metal gears. Liquid Snake's demands are pretty basic actually. He just wants a lot of money, and the remains of big boss. His real goal, is to recreate Outer Heaven, big boss's country for mercenary soldiers. Liquid believes that soldiers are becoming insignificant to the government, and he wants a place for soldiers, people like him, to fight. He believes that if the us wasn't going to give soldiers a purpose to live their lives, he was going to wage war himself, and give them a reason to live their lives. With metal gear rex, a large amount of money, and big boss' remains (he could create more genome soldiers using big boss' genes) he could recreate outer heaven and give soldiers a place to fight.
Solid Snake, who defeated Big Boss years and years ago, is called out of retirement to stop Liquid Snake, and also rescue hostages at shadow moses. He soon discovered that Shadow Moses was harboring another Metal Gear, and it then became his mission to destroy it. In the process, he once again comes in contact with gray fox, his companion and best friend who he believed to be dead. Grey fox fights snake in order to "feel alive" again. At the end of the game, snake destroys metal gear, goes off with otacon and gray fox's last words have a huge impact on him. Snake then decides to fight for what he believes in, and that's what leads him to mgs 2...
MGS 2: You play as Raiden, a green soldier with no real experience. Raiden's goal is to infiltrate the big shell, and eliminate dead cell and solidus snake, and save the president and hostages. he blindly follows his orders.
Solidus Snake is the last clone of big boss, and he is the one that has taken over the big shell. his goal is to overthrow the patriots, who he works for, but is planning to rebel against. (i'll get to the patriots later) solidus' goal is to capture arsenal gear, use it to launch a strike over NYC, and devestate a huge part of the patriots' control: the economy. then he would expose the patriots to the world, and america would be free again from the control of the patriots. what he didnt count on, however, was ocelot turning him in to the patriots.
Ocelot works for he patriots, and lets them in on solidus' plan. the patriots then use this to manipulate solidus, and set up the big shell events. turns out, everythingg that happens in MGS2, the entire big shell event, is a simulation set up by the patriots, in order to make raiden into the perfect killing machine, aka solid snake. it's a replica of shadow moses, what solid snake had to go through. it's called the S3 plan. a solid snake simulation. by combining real world experience, vr training to get rid of weak emotions, and simulating what solid snake had gone through, the patriots would have the perfect soldier. lol only problem was, the real solid snake showed up at the big shell, which prevented it all from happening. the patriots knew they had to wait till solid snake was dead so he couldnt interfere, because there could never be 2 solid snakes. snake faked his death, which is why the patriots went ahead with this.
The patriots are the driving force behind the Metal Gear Solid series. everything that happens comes back to the patriots. people work for the patriots, people try to rebel, but in the end the patriots control everything. they began as the philosophers (the most wealthy and powerful people from china, russia and america), but then they all died, and the remaining are called the patriots...becasue the original "wiseman's commitee" are all dead, the player really doesnt know what the patriots are. there are many theories, but theres not one solid theory. anyways, rule of thumb to always keep in mind while playing metal gear: Ocelot always works for the patriots, no matter what you think. this will make things much simpler.
lastly, why i'm so excited for MGS4...Snake is setting out to find the patriots, and destroy them. I am so intrigued by the patriots, this is really going to be the best finale to any game ever...