The principle for serial exhaustive extraction is that you start with a non-polar solvent to a moderately polar and finally polar solvent. The number of solvents you would use depends on the difference in polarity on the polarity scale e.g you can try hexane - dichloromethane - ethylacetate - Methanol.
Serial extraction is straight forward as mentioned by other researchers. But the question is what you want to extract out. First think about this, otherwise you are going to loose solvent and precious time. If you are looking for phenolics may be you can try polar solvents, especially hydro-alcohalic solvents. I recently published a review "Review of Procedures Used for the Extraction of Anti-Cancer Compounds from Tropical Plants". You can have a look to get some idea..
You have to begin the extraction with a non-polar solvent (hexane) and after increase the polarity of the solvent. For instance ethyl acetate followed by methanol. Acid -base extraction can be used in several cases (alcaloids, ...)
As all researcher comments you have to start with non polar solvent like hexane and after increase the polarity using a mixture with the next solvent. For example if you use
hexane- dichloromethane - methanol, you start with only hexane and then a mixture containing hexane and dichloromethane , for example 9:1, 7:3, 5:5, 3:7, 1:9 and then pure dichloromethane and continue with the mixture of dichloromethane with methanol and so on.