Separate your rings into two equal piles for your two earrings. There should be 5 tiny rings, 4 small rings and 4 large rings for each earring (as well as an ear wire).
Start by closing all the tiny rings.

Open one of the large rings and link it through 3 tiny rings.
Double your large ring by opening another large ring and threading it through the 3 tiny rings, but not the first large ring. Your large rings will lie parallel to each other.

Open another large ring, thread it through 1 of the tiny rings already woven into your earring, then add 2 loose tiny rings to the ring you just added. Close this ring, and double it like the other large ring.

Open a small ring and link it through 2 tiny rings, one attached to each big ring. Double this small ring.

On the other side, link another small ring to the last 2 hanging tiny rings. Before closing this ring, add the earring hook just like another ring. Close this ring, then double it with another small ring.
Repeat for the second earring. Celebrate by wearing your new pair of tiny bubbles!

For a matching bracelet, just chain together these bubble units (I used 19g 5/32" rings, but anything with an ID bigger than 1/8 will work just fine).
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Information on Jump Rings:
All wire and jump rings on wirejewelry are measured in AWG.

If you have precious metal jump rings, use

Tiny: 20-gauge (AWG) 3/32" (5 for each earring)
Small: 19-gauge (AWG) 5/32" (4 for each earring)
Large: 19-gauge (AWG) 1/4" (4 for each earring)

For SWG gauge:

Tiny: 20g (SWG) 7/64" (5 for each earring)
Small: 18g (SWG) 5/32" (4 for each earring)
Large: 18g (SWG) 1/4" (4 for each earring)

Note on Jump Ring Gauges: Precious metal wire is commonly measured in AWG (American Wire Gauge), whereas some base metal jump rings are measured in SWG (Standard Wire Gauge, also used to measure guitar strings and some electrical wiring).