The following procedure is based on one provided by Bev Purnell and from Current protocols.  I've provided an optional spermine precipitation because agarose often leaves impurities that can inhibit various enzymatic manipulations.  If you choose to skip the spermine precipitation, simply add 1/10 volume of 3 M Na Acetate and 2.5 volumes of 100% ethanol to the combined aqueous phase.

1. Restriction cut up to 10 ug of DNA in a final volume of 50 ul.  Check 50 ng on a minigel to insure complete digestion.
2. Melt low melting point agarose in 1X TBE.  A typical gel for resolving fragments of 1 kb or greater is 1%.  Add ethidium bromide to 1 ug/ml.  Assemble the gel with wells that are 1 cm wide.  Pour the gel in the cold room.  Allow 30 minutes for the gel to polymeraize.
3. Run gel at 100 volts in the cold room.  Separation of fragments can be visualized with long wavelength UV light from a hand-held lamp.
4. Cut out the desired bands and place them in eppendorf tubes.
5. Melt the agarose at 70^oC and add enough TE to reduce the agarose concentration to less than 0.4 %.
6. Add an equal volume of buffered phenol (not phenol:chloroform) and shake for 5 minutes are room temperature.
7. Spin at top speed in the microfuge at room temperature for 10 minutes.
8. A substantial interface may be evident.  Transfer as much of the aqueous phase to a new tube and rextract the phenol phase and interface with an equal volume of TE (shake 5 minutes, spin 10 minutes).
9. Collect the second aqueous phase (add to the first aqueous phase), and reextract the phenol layer a third time if a substantial interface is still evident.
10. Estimate the volume of the combined aqueous phases and add 1/10 volume of 100 mM spermine.  Mix and place on ice for at least 15 minutes.
11. Microfuge sample at top speed in the cold for 15 minutes.  Transfer the supernatant to a fresh tube and set this aside.  The DNA should have precipitated, but save this supernatant until your certain you've recovered DNA from the precipitate.
12. Dissolve the precipitate in 100 ul of 0.6 M Na Acetate pH 6.  Heat to 37^oC and agitate intermittantly for 15 minutes.
13. Add 100 ul of water and 500 ul of cold 100% ethanol.  Mix and place on ice for 15 minutes.
14. Microfuge sample at top speed in the cold for 30 minutes.
15. Discard the supernatant and add 200 ul of cold 75% ethanol to the precipitate.  Splash the ethanol around inside the tube, microfuge in the cold for 5 minutes and discard supernatant.
16. Dry the sample and then dissolve it in 20 ul of TE.
17. Determine the DNA concentration using the fluorometer.
• If there is no DNA, it is possible that the DNA failed to precipitate with spermine.  Take the spermine supernatant and add 1/10 volume of 3M Na Acetate and 2.5 volumes of Ethanol.  Perform the ethanol precipitation as described above.