Just like every other Souls game, some spots are just better than others for farming Runes- either by giving better Rune payouts per enemy or by having just enough enemies to mow them down and get enough to buy more levels.
Elden Ring has you trade in Runes to buy more levels, with the amount required going up with every level. This guide is a great spot for farming in the early game, with the only pre-requisite being you’ve killed Margit, The Fell Omen first.
The best spot to farm runes in Elden Ring is by the Limgrave Tower Bridge site of Grace, which you can unlock if you decide to go through the main gate of Stormveil castle instead of taking the long way around. Once you see a fork in the road simply turn right into a separate building, and go straight to reach the Site of Grace.
Now comes the hard part- just past the Site of Grace are three Golem enemies, which can be intimidating for fresh players. If you’ve sucessfully killed Margit, The Fell Omen though, I have no doubt that you’ll be able to make short work of them.
Getting rid of the Golems is easy- simply two-hand your weapon (hold triangle + R1) and do jumping heavy attacks on their ankles until they fall down. You’ll want to stay out of the way of the other golems, particularly the bowman trying his best to audiition for Anor Londo. Depending on your weapon, you should do enough poise damage over time to knock the golems over, which will let you do a critical hit on their chest, taking a huge chunk out of their health.
Once all three golems are dealt with, you should get approximately 3K Runes. This is a huge amount for newer players, and mastering the technique for killing the golems means you’ll be able to do this in less than 4 minutes meaning you can just reset the Site of Grace to keep going and easily make enough to level up multiple times.
Leveling Up Your Weapon
To level up your weapon, you’ll need access to Smithing Stones. Thankfully, Elden Ring gives plenty of ways to get them for early players. There are two dungeons in the game, called Limgrave Tunnels and Morne Tunnels, that are full of Stonediggers. These Stonediggers have a chance of dropping Smithing Stones, but also remember to see where they’re digging- if their area is gold, there’s an extra smithing stone there, too.
Getting your weapon to a high enough level that you no longer need Smithing Stone  is a good way to also help yourself kill the golems, which means more souls for you. You’ll be able to upgrade your weapons up to +3 at the Church of Elleh, and each of the tunnels will give you enough stones to upgrade your weapon to +3.