1. You can quantify DNA/RNA by spectrophotometric method taking absorbance at 260 nm. Calculate OD260/OD280 ratio for an indication of purity.
2. To quantitate DNA, run the samples on a 1% agarose slab gel containing 0.5 μg/mL ethidium bromide. Also run DNA standards of known concentration. Use a UV light to take the gel image. Compare fluorescence intensities and estimate the concentrations.
3. DNA/RNA quantification can be performed by instrument Qubit fluorometer, using ds DNA/ss DNA or RNA assay kit.
4. DNA/RNA can be quantified using NanoDrop instrument.
There are various methods of nucleic acid quantification as mentioned in the above answer. This paper here compares the efficiency of various methods. The basic protocols are also given.
Article Comparison of DNA and RNA quantification methods suitable fo...