The Space Race entails a time when the United States and the former Soviet Union (commonly referred to as the USSR) were competing over who would conquer first the ultimate task of reaching the outer space for exploration. 

Your speech has to follow a format depending on what it is intended to do. 

• inform
• entertain
• persuade
• instruct

If you are going to make a speech that informs people on what is the Space Race, then here are some suggestions.

1. Start with an opening statement that catches the audience's attention. You may use a quotation that you later will tie-in to the body of the speech, or an interesting fact about the Space Race that you will equally tie-in at some point. Some students like to start with a question such as: "Who was first?" or "So, who won the Space Race?" as starting points.
2. Your introductory paragraph MUST point out what you will be focusing on in your speech. The after the introductory sentence, write the MAIN IDEA of your speech: the Space Race was a time when (whatever happens). Leave that sentence alone and continue with a statement that also reflects the theme. For example, explain WHY this was a big deal at the time. This would be your second sentence. Then explain WHO was involved in it happening (government, the economy, scientists, etc). Finally summarize the outcome of the Space Race in one sentence. 
3. Your second paragraph should expand on what you said in your first statement (what exactly is the Space Race). Here, you can comfortably explain what it is, why it is called that way, when it happened (explain that both were world Super-Powers), how we felt about each other (the US thought the Soviets were basically otherworldly fiends) and what winning the Space Race would entail.
4. Your third paragraph should expand on what you said in your second statement (why was it a big deal). Reflect on the political, social, even entertainment environment of the time. These were times of deep psychological and social change in the overall society.  Notice how this paragraph extends the last sentence of your first paragraph, making it a wonderful transition statement to lead to this point. 
5. Your fourth paragraph should now focus on what and who were the pawns in this game. Who were the two presidents, how important they were, whether there was any publicity on this, who won the media wars, who were the astronauts, basically, state the "competitors" of the Space Race and when they were going to have a showdown.
6. Your fifth paragraph will explain the showdown as concisely as possible. Who did what? When was it done? What equipment was used? How did the media respond? Who, in your view, did the best job?
7. Your conclusion is a final paragraph where you reflect upon what you just said, and you answer the question of who won the Space Race, or what you think of it according to what you said (not just based on your opinion as it is not stated in the documentation).

As you can see, a speech is no different than an essay. The only thing that you will find is that an essay has to summarize with powerful and informative sentences a very good amount of information. If you ever do a research paper you will understand the difference between how one paragraph in a speech of essay can harbor so much data without detailing to an extreme. The more you write essays, the more you will get a gist of the information that the reader and the writer are supposed to share.