QIAGEN purification kit works for DNA > 100 bp. QIAGEN gel extraction kit works for DNA > 70 bp. Here is a protocol for purification of small DNA fragments (for example from PCR or primer extension):
1. Run solution on a gel to separate the DNA from other molecules.
2. slice out the DNA band with a razor.
3. place the slice into a pre-weigher eppindorf tube. You can weigh the tube again to get the weight of the gel slice. Then you can calculate the volume of the slice using the density of a 1% gel, which is similar to that of water (1 mg/uL).
4. Mash up the gel slice in the bottom of the eppindorf tube (I did this by pressing it down with the tip of a sterile plate spreading stick).
5. Add 500 uL TE buffer to the tube. And leave it shaking overnight (i used 750 rpm in the eppindorf thermomixer at room temp). The next day, the concentration of DNA in gel/TE should hopefully have reached an equilibrium.
6. Extract the TE by spinning down the gel in the eppindorf tube for 30 minutes at maximum rpm and pipette out 450 - 500 uL of the solution into a separate eppindorf tube (use nanodrop to measure concentration at this point).
7. Run ethanol precipitation (as follows):
7.1 add1/10 volume sodium acetate to the solution
7.2 add 2 volumes of absolute ethanol (pre-chilled at -20).
7.3 let incubate for 1-2 hrs at -80 (the smaller the size/concentration of DNA, the better it is to leave it incubating longer.. i used 2 hrs and then left it at 4 degrees for another 10 min)
7.4 centrifuge at max rpm for 30 min at 4 degrees (I moved the microfuge into the cold room for this).
7.5 aspirate the ethanol from the DNA pellet (get as much as possible without disrupting the pellet).
7.6 wash with 1 mL 70% ethanol (pre-chilled at -20). To do this part, slowly pipette the ethanol over the pellet, then slowly invert the tube back and forth. Try not to break up the pellet.
7.7 Centrifuge the pellet back down at max rpm for 2 min.
7.8 remove the ethanol from the pellet (I did this by aspirating most of it with a pipette and then using a speed vac (unheated) the evaporate the remaining). Caution: If the pellet gets too dry, it becomes difficult to resuspend it.
7.9 resuspend the DNA pellet in water to desired concentration.
8. store at -20