Check the library. Older speeches by prominent figures are often transcribed and included in various non-fiction books. Ask a librarian where a certain figure's speech may be found in the non-fiction section of the library. Librarians are trained to know a vast amount of information, as well as how to obtain it. If searching the library for a book that features the speech leaves you empty handed, utilize the librarian's searching abilities and ask them to help you or for suggestions on where else the speech is correctly featured. Although very recent speeches will not be found in a book just yet, a librarian may have an idea of where you can find a transcription.
Look in a textbook. Certain textbooks feature entire speeches by prominent figures, particularly if the speech correlates with a turning point in history. Flip to the back of a textbook that the prominent figure is likely featured in, such as a history book. Look up the last name of the figure in the index. Often textbooks indicate whether or not a prominent figure's speech is featured in the textbook by listing the title underneath the figure's name.
Search reputable websites. Academic search engines stay up to date with politics. For instance, inputting "Obama Speech 2011" into an academic search engine pulls up a series of reputable websites that feature the most recent speeches that President Obama has given. Academic search engines filter out bad references or manipulated speeches.
Watch or listen to the speech. When speeches given by prominent figures are posted online, many times as the speech is given, a transcription is available. Referring to the speech as you read the transcription ensures that you are reading the correct and original speech.