Once the ionic liquids are formed, it will be relatively difficult to purify them.
So it is rather easy to start with raw materials with maximum possible purity to ensure that relatively pure product, that is, ionic liquid is formed out of them.
As previous answer, it is critical to start with pure materials. For removing the impurities, you should work with solvents. You know the structure of your ionic liquid and the impurities. You should find a solvent (or a mixture of solvents) which dissolve your product or side products.
What Mr. Bandyopadhyay stated is definitively the case for ionic liquids, they are usually very hard to purify, so make sure you are synthesizing them with pure raw materials. One of the simplest purifications that can be made is to clean them using ethyl ether (If your IL is not soluble in ether and your impurities are). Their viscosity can definitively be an issue, but you can usually work with them at higher temperatures (which reduces their viscosity considerably) with no worries about degradation and other problems. Volatile impurities can also be removed by heating them in a vacuum, since they have negligible vapor pressure even at high temperatures (In some cases ILs can be heated up to more then 300 °C without any problems). It is also very hard to separate non-volatile polar compounds from polar ionic liquids, since you can't do a simple solvent extraction or heat it up to drive off any volatile impurities. Of course, without knowing the specific IL you are planing to purify, we can't really help too much, just give you some trends of ILs in general.
Of course, it will depend on the nature of both the ionic liquid and the impurities. Also in the expected level of purity.
Extraction with an adequate solvent; evaporation under high vacuum and heating; recrystallization of the IL if possible; precipitation of undesired salts with dissolution of the IL in a suitable solvent + filtration; adsorption of impurities with activated carbon + filtration; distillation of the impurities; column chromatography in alumina... all those techniques can be helpfull depending on your system, your needs and the materials and equipment at your disposal.
Volatile impurities can also be removed by heating them in a high vacuum pump and the best way of purifying the ionic liquids are distillation.I had distilled triazolium based ionic liquids in my research work.
Another option as to remove the starting materials based on its solubility in organic solvents or mixture of the solvents. As my opinion ionic liquids are insoluble in hexane and 10% ethyl acetate. hence, to tack a mixture of solvents to remove the unreacted impurities then you will get purified ionic liquids. whenever you preparing the ionic liquid you should was with toluene at least thrice to remove the starting materials, most of the starting materials are soluble in toluene, but not soluble in ionic liquids.
It is really a big problem for the purification of ionic liquid. I suggest, you may use relatively less polar solvent like diethyl ether or ethyl acetate to wast them. Generally, ionic liquids I have used in my research, forms separate layer between the ionic liquid and solvent (like ethyl acetate). I have taken the ionic liquid and solvent in a 50 ml centrifuge tube and one magnetic bead. Over night stirring under close cap condition will helps the impurity to go into the washing solvent. Repeating of this process for 3 or 4 times results in the NMR pure ionic liquid.