Organic Chemistry Toolbox! (For those pesky OH groups)
Water or Neutral OH: Feel free to do you E1 and SN1 mechanism, except when there is heat. Only E1 will happen if there's heat.
Need to make your OH a Leaving Group?
Tosylate + Cl: RETAINS STEREO CHEMISTRY, bonds with the H and acts as a leaving group entirely (How to remember? Oh this shit (Ts = Tosylate) retains streochemistry)
PBr3: CHANGES CHIRALITY (R->S or S->R), turns your OH into a Br, which is a good leaving group
Deprotonate OH (FOR SN1): Turn it into a nucleophile for your SN1 reaction with Na+H. H will attack the H on OH, making O-. Now, it's a good nucleophile.
Acid Catalyzed Dehydration of an Alcohol (FOR E1): Have your starting material do an Acid-Base reaction with the acid, turning OH into H2O. H2O is a good leacing group, so you can continue with E1.