Rat-Slayer
For all you noobs in runescape that can't wait to level up, I have discovered a quick and easy way to do so, although it takes a bit of patience. When you first come into the world of runescape (after the tutorial island), you appear at the Lumbridge town square. If you look around a bit, you will find an abundance of small rats. These rats are extremely easy to kill, but make you experience just the same. Every time you kill a rat, you gain 8 experience in the current attack type. If you go to the stats page, and mouseover one of the skills, you can see the progress to the next skill level. Divide this number by 8, and you get the number of rats you must kill to progress to the next level of that skill. To advance your combat level (the level beside your name), you must gain a level in three of the attack skills. This can be all one skill, or three different skills. Hitpoints count too. I went from level 8 to level 21 rather quickly using this rat-slaying method.
Multitasking with Goblins
If you want to levelup while doing something else, you should make your way to the forest near lumbridge with an abundance of level 2 goblins. They take a while to kill but aren't very deadly. When you find them, click on one, then switch to your other program. Use the other program until a few seconds after you hear the goblin die, then quickly switch back to RS and click anothr goblin, then back to your other program. This is not as effective or precise as the above rat method, but its a good way to levelup while multitasking.
Warning
Don't beg. There are very few kind-hearted high level players that will give you even 10 gold. I once gave a beggar 2k because he pleaded for it, but most people will not do that, so don't even try.
Grand Exchange
The best way to get money is through the Grand Exchange (ge), which is west of Varrock. Depending on the day's demands, certain things will get you rich and certain things won't. I once made 6k by buying flour and water and mixing them into pastry dough. The next day, no one was selling flour and no one was buying pastry dough, so that method was useless. Here is a list of some of the money-making methods I have discovered:
(Buy buckets and flour -> fill buckets with water from nearby fountain (to the east) -> Mix into Pastry dough -> sell through GE auto-exchange
(Dump all your items in the bank -> buy 32 empty buckets -> fill with water from fountain -> sell at max price
(Dump all your items in the bank -> buy 32 empty pots -> travel to mill and fill pots with flour -> return to GE and sell for max price
(Sell ashes sitting around on GE floor
(Just wait around for someone to abduct you! If you win their minigame they'll most likely give you gems.