Creating an ombre look at home is fairly easy with the right equipment and a little patience (an extra set of hands doesn't hurt either!). Whether you want to create the popular light-to-dark ombre as modeled here by Jessica Biel, or something more bold like the pink I added to my bleached tresses the steps are the same. It just takes some dye (or bleach), some strips of foil, and a paint brush.

I bleached and toned my hair before starting. Then I used a crazy bright pink dye to achieve the ombre effect.
These are the materials I used:

Hair Bleach (peroxide)
Toner to make it less brassy
Dye brush
Squeeze bottle (you could use a mixing bowl or cup)
Splat hair color in Pink Fetish (they also make blue, red, and purple) - this kit comes with bleach
Plastic wrap
Aluminum Foil
Deep conditioner

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Step 1: Sectioning

Section off the area of hair you want to change.
Protect the rest of the hair from getting bleach or dye on it. In my case, we slathered deep conditioner on the hair we wanted to leave blonde, and then wrapped it all in plastic wrap!

Step 2: The First Layer

Using a comb or the opposite end of the dye brush, section off a thin line of hair.
Place foil underneath hair.
Apply dye or bleach to entire length of this section of hair.
Wrap in foil.

Step 3: Ombre Layers

Repeat process, leaving more and more hair untreated as you move up, until you are just painting the tips.
For a very subtle ombre, apply dye to tips of hair, rinse brush, and blend color further up hair towards roots
Let dye or bleach process for recommended amount of time.
Remove foils, but keep rest of hair protected as you rinse the product out.
Condition well.

Step 4: Go Nuts!

If you're using a bold color like mine, understand that some of it will rinse out with each wash, and designate a special towel for this purpose! If you're bleaching from dark to light, then you won't have a problem.

Have fun and be sure to post your pictures if you try it out!