Generally, a good way of starting a speech is by giving an attention-catching fact; if possible, relate it at the same time to the reason why you are giving a speech.
For example: "Next year, we will be commemorating 45 years since the Stonewall riots."; "Twelve years have passed since the first same-sex marriage has been officiated in the Netherlands; as of now, 14 more countries have followed suit", "This month, Hawaii became the fifteenth state to grant support to gay marriage".
Move on to presenting why the issue you are talking about is important, and what you wish to argue for, then to the body of your speech.
For example: "This month, Hawaii became the fifteenth state to grant support to gay marriage. This is cause for celebration among those of us who support marriage equality, but there is a long way to go: 29 states still have constitutional provisions that limit marriages to one man and one woman and continue to deny the freedom to marry to gay and lesbian citizens. You might wonder: why should we care about this issue? I'd say it is because..." [insert starting argument or give an overview of what it means, practically, not to be able to marry your spouse of choice- for example, if your partner is foreign they may be deported; then continue with the rest of your argumentation]/