Whatever your interest—birth, death, or marriage certificates, old addresses, military records—spend a couple of days researching the archives, indexes, magistrates, memorials, ministries and embassies in your cities/states/countries of interest (see Tip 8 for some specific examples of the resources I’ve used).
Many of these archives (e.g., the U.S. and U.K. National Archives) are searchable online and some are even happy to do the searching for you if you send an email with the appropriate information (I will forever be grateful to Irena from the Hoover Institution at Stanford, who helped me track down a hand-written account of my great-uncle’s, and to Ms. Kroll at the UK Ministry of Defense, who sent me stacks of military records pertaining to relatives who fought for the Allies in conjunction with the British Army). Read the fine print—typically these organizations post instructions on their sites on how best to contact them re: acquiring records. Pay close attention, and note that some institutions abroad may require emails/letters in their native language.