Well no one was born knowing electrical wiring. I sure wasn't (although I started right in at age 3 when I took apart an electric train to see what made it go...)
Anyway there are many ways to solve your situation.
One way is to learn how to do drywall. Very easy and quite cheap. But an art. Anyway once you know this, you can cut out a portion of wall - say 1 ft. square, then replace an existing electric outlet with a large deep double gang electric box with a single gang "plaster ring". Then suddenly you have all sorts of room in that box for making electrical connections.
And you can more easily fish a wire up to where you are going.
When you make wiring connections inside an electrical box and have say 2 wires to connect to only one connection, the way to do it is using what is called a "pig tail". You take a 3rd short length of wire, then twist the 3 wires together and use a "wire nut", then attach that 3rd wire to the connection/screw on the outlet.
Then junction boxes in an accessible place like an attic or crawl space are a good idea to make splices. Just be sure you can get to these boxes in the future for troubleshooting or whatever. (Don't burry these in a wall where you can't get to them.)
If you want to learn more about electrical wiring, might want to pick up a book at a home improvement store. Or more advanced books here...
http://www.buildersbook.com/Merchant2/merchant.mvc?Screen=CTGY&Store_Code=bbi&Category_Code=40
There are all sorts of electrical boxes. Some can be installed by just cutting a hole the size of the electrical box in the drywall. I don't know if there are double gang boxes like this?
Then another trick is to use 2 junction boxes in the attic. Cut the wire, then use 2 junction boxes and a length of the same type wire to reconnect them and use one of them for your new connection.
ALWAYS turn off the main power to the house before working on any electrical wiring. There are circuits called "Multi-Wire Branch Circuits" where two separate circuit breakers control the wiring in one cable! If you just turn off one breaker, the other wiring will still be live! So turn off ALL the power to be sure everything is off.
Then also I would suggest reading one of those wiring books cover to cover before doing any wiring. Then you will understand the wiring in your house better. And will understand how to best install new wiring so it is safe.
A good thing to do is get an electrical permit for any electrical work you do. With this, you get an expert to look over your work to be sure it is safe. And the cost is cheap as opposed to hiring an electrician to look over your work.
And what are they going to do? Find something which is not safe and ask you to make it safe? Good! That's the idea!
Plaster ring...
Pig tail...