Blood Echoes can be used as both experience in order to level your character, as well as to purchase items from bath messengers. You will obtain them by killing enemies, bosses or using coldblood consumable items.
Farming Method 1
warp to Witch's Abode then run backwards all the way where that shadow beast spawns. the most important thing here is to use the Heir and moon rune, especially Heir as it increases the echoes you get from visceral kills and its really easy to do it on the executioner guys which will be the bulk of your blood echoes.
when you are done with the run, i would suggest you to use Bold Hunter's mark and rinse and repeat.
Another easy way to farm would be to go to the Nightmare Headstone, and go to the Mergo's Loft - Base awakening lamp. From there, head up the stairs towards the broken cage, and go down and jump off at the broken window. From there head onto the path of the brain heads, and just kill them. You can gain over 30,000 Blood echoes per run if you do this. Easiest way to kill them, and make sure you don't lose your health from frenzy is to Visceral attack them. However, if you don't feel confident in that, I suggest bringing a lot of sedatives so you don't die from frenzy. If you wanna earn more, I suggest having the Heir rune and the Moon rune. This is more for end game, but it's still viable.
Farming Method 2
This method requires access to the Lecture Building, which can only be access after receiving the Tonsil Stone.
The rifle spear is recommended for this method because of its thrust damage and long range.