This quest doesn't require any fighting, but is very tedious
because it requires a lot of running around all over the place.
If you're a beginner, start off with an easier quest such as
Sheep Shearer or Cook's Assistant.
To launch the quest, talk to Juliet who can be found in her
large house to the west of Varrock. She is on the upper floor,
on the balcony. Talk to her and she will give you a message to
deliver to Romeo. Take it and head to the center of Varrock
(where the fountain is). Romeo should be around there somewhere.
Give him the message.
Next, Romeo will tell you to see Father Lawrence. The latter is
in the church at the very northeast of Varrock. Go there and
talk to the Father. He will tell you that the only way to solve
Romeo and Juliet's problem is to make a potion that will put
Juliet to sleep and make her appear dead. He tells you talk to
the Apothecary.
The apothecary's shop is located in southwest Varrock, near the
sword shop. It is denoted on the minimap with a vial symbol.
The apothecary will tell you to get some cadava berries for the
potion. These berries can be found outside the south wall of
Varrock. Go there, pick some (you only need one bunch, actually),
then hurry back to the Apothecary. Give him the berries and he
will give you the potion.
Take the potion back to Juliet. She will drink it and "die".
Now all you have to do is go back to Romeo and tell him what
happened. The rest of the quest is one big cutscene where you
don't have to do anything. Mission accomplished!