First off, get used to working in tight spaces!
You should always handle the leads by the plugs on the ends, never pull on the leads or bend them excessively or you will damage the conductor inside (or rip them off, as you have discovered).
I would try and get some long nosed pliers on to the rubber remnants and use a twisting action to break the bond and loosen it. Try not to snap the end of the spark plug when you do this.
When removing the spark plugs, use a proper spark plug socket (deeper and has a rubber insert to prevent damage to the plug) with an extension bar and rachet. Ensure the socket is perfectly square on the spark plug and do not allow the socket to 'tilt' or you risk snapping the plug. Although you are replacing them, this is bad because the broken ceramic fragments can fall into the cylinder upon removal of the plug and will damage the cylinder wall.
Make sure you apply consistent torque, and if the plug feels loose for half a turn or so and then becomes tighter during removal there may be a crossed thread - do stop if this happens and have a more experienced friend or relative take a look if you cannot afford a garage.
If you do break a plug, use a vacuum to get the bits from the surrounding area and the spark plug seat ideally with the plug still in place so the bits cannot fall inside the engine.
Insertion of the spark plug should initially be with the extension bar and socket ONLY until the thread is properly engaged. If you are careful you will avoid crossing the thread. You should be able to get 4 or 5 turns by hand without the use of a ratchet. Do not over tighten the plugs, when you feel a significant change in resistance they should be done.
Make a note of which lead goes to which plug, paying attention to the coil pack end as well. Not not bend the leads excessively trying to make them look neat. The spark plug end of the lead may feel like it makes a 'click' as it engages onto the end of the spark plug.
That's pretty much the basics, maybe other people can share their tips and experience.