You will need litmus paper, acid (such as "muriatic" [hydrochloric] or sulfuric), base (lye is good), and a nonpolar solvent (benzene, toluene, or xylene are all good.)
This is a simple acid/base extraction that is pretty standard for alkaloids (of which nicotine is one.) It will yield pure crystal nicotine HCl. If you use sulfuric acid then you will get nicotine sulfate. Both are salts of nicotine and are pharmacologically similar. The average cigarette contains 1 milligram of nicotine, so keep that in mind when dosing your final product with crystal. Nicotine is a very potent drug! It only takes a few milligrams to make someone sick.
Here it is:
1) Take tobacco and mix it with distilled water. Make the tobacco water acidic to litmus paper (only a few drops of HCl needed.) Pour off the water and save it. Repeat this two or three more times, until the water is not so dark. Combine all of the water extract. Now the acidic (protonated) form of nicotine is in the water. There is also a lot of other crap there, too.
2) Add lye-water dropwise to the acidic tobacco water until the water is alkaline to litmus. Now the acidic form of nicotine has been converted to the "free base" form (deprotonated.) It is now more soluble in a nonpolar solvent than water.
3) Add about a half volume of nonpolar solvent (benzene, toluene, xylene) to the alkaline water and gently mix. If they are mixed vigorously you will get an emulsion, which is a nightmare to separate if you don't have a centrifuge. Anyway, mix gently, such as slowly inverting the mixture in a closed bottle repeatedly. As long as two distinct layers are forming when the bubbles settle down you are in business. Pour off the top layer (the solvent.) Repeat this two more times. Combine the solvent. Now the free base nicotine is in the solvent and is relatively pure. But we need the salt of nicotine, not the free base.
4) Take about 2 volumes of distilled water and make them acidic by dropwise addition of acid. Use this water to extract out the nicotine from the solvent. By mixing the water with the solvent in the same manner described above the nicotine will now dissolve preferentially into the water. Extract out the nicotine with the acidic water 3 times. Combine the water. Now (slowly!) add dropwise lye water until the pH is neutral (7). Evaporate the water. The yellow crystals left behind are pure nicotine HCl. Protect them from light when storing as nicotine is photosensitive. Have fun!