To be honest.... a critical factor in designing a weight lifting routine is progressive overload. All this really means is, for a program to be successful in increasing strength, muscle mass, etc.... it must provide a stressor to the
body beyond what it's used to in order to elicit a positive adaptation.
When people go out and buy one or two sets of light dumbbells, they lock themselves into training without progressive overload.
No progressive overload = no positive adaptation.
That said, your purchase wasn't fruitless. You can build up a base of conditioning through calisthenics. Once you become acclimated to calisthenics, you can throw in your DBs for a little progression.
Beyond that though, you're going to have to find new ways to challenge your muscles.
Joining a
gym is out of the question?
If so, I'd consider buying some home equipment if space is available.
What exactly are your goals?
And what are your stats?
As a quick note, I wouldn't focus on training the arms at all. You want to focus on
exercises that give you the most bang for your buck. These are the
exercises that call on the most muscles/joints to execute.
These are commonly referred to as compound exercise. Think:
Legs: Squats, deadlifts, lunges, stepups
Chest: Presses, flys, pushups
Back: Rows, deadlifts, pullups
Shoulders: Overhead Pressing
Core: Crunches, planks, hyperextensions, etc
These are just examples. You can go to something like
Workout Routines & Exercises - New iPod Videos! to find examples of compound
exercises. You can even sort by what sort of equipment you have available to you.
Eventually my site will be up with, what I'd consider good, instructional videos for as many
exercises we can think up.