You can find links to recent and historic speeches posted on the Internet through the Online Speech Bank, or use a search engine (or two) to check for the speaker by name and by his/her business/agency/etc. Also check YouTube for videos.
Alternatively/In addition, call the speaker's office, agency, company, etc.
U.S. Government: Speeches by U.S. government officials are often available through the Federal News Service file on the FNS Web site, Lexis (GENFED;FEDNEW) and Westlaw.
In addition, Morningside Partners (formerly the Federal Document Clearing House or FDCH, now operating as CQ Transcriptions,) provides transcripts of Federal political events, speeches, etc. Morningside/CQ material are available through various vendors (check Lexis, Westlaw, Factiva, CQ Roll Call, etc.).
For videos of Congressional hearings and speeches by Senators and members of the House of Representatives, check the C-Span Video Library. For more sources, see News - Television & Radio - Transcripts and Recordings.