Because Demon's Souls is such a tough game you need all the help that you can get.
The way that you level up in this game is a little different to most RPGs (Role Playing Games).
Instead of killing enemies and gaining experience, killing enemies in Demon's Souls rewards you with souls, which must then be traded in the Nexus with the mysterious black witch in exchange for stat points.
Because of this, it's important that when trying to gather souls that you don't die before you make it back to the Nexus (since you'll drop all of the souls you were carrying at the time).
The best spot that I've found to gain souls is on level 4-2 (named 'The Shrine of Storms').
What you need to do from the starting point is to run forwards, drop off the ledge, turn around and run down the corridor to the cliff edge.
From here you need to get out your bow and quickly shoot the Reaper (the White Bow works the best since it kills in 3 shots).
As soon as you've done this, turn around and run off the cliff at the other end (thus killing yourself), since this means you'll respawn at the start and the Reaper will be there again for you to kill.
This works great because you can run back and forth and you can gather around 100,000 souls in 15 minutes! One way that you can increase the amount of souls you are given is by equipping the 'Ring of Avarice'.
This ring can be bought in level 3-1 for 50,000 souls from the shop keeper.
This ring will increase the amount of souls you're given by 20%, and is well worth what you'll pay for it.