How do I start a compare/contrast essay when the subject is to compare the Spanish and British and how they colonized?

Introduction of any essay must serve two purposes. First, it must provide the reader an idea about the subject being covered in some detail. For example in this case of yours the title of the essay itself may tell what the subject, but you will need to give additional information on scope of essay - for example, the period in history covered, will it cover just the method of colonization or also the way colonies were administered subsequently, and so on.

Second, function served is to establish the importance of your essay, or to get the reader interested in reading the essay. For some readers the description of subject it self may be enough to attract them, but in other cases it may be better to say something about why it is worthwhile for the reader to know the comparative methods of colonization used by Spanish and British.

I do not know what will be contents of the main part of your essay, and that is not a part of your question. But I would like to point out that the introduction depends very much on the contents of the main body. In many large essays and dissertations, the introduction may be the firs part of the work but actually written in the last. If your essay is small enough you will have fairly clear idea of what is to come in the main body, and thus it may be OK to start with the introduction. But if you have the time and inclination you may review the introduction after main body is written.

You could start off with some context, something general about how the European nations became involved in colonization on a large scale starting from the 1400's. Then bring Spain and Britain into the picture, naming these two countries as two major colonizers. Then you should go right into your thesis statement, which should clearly state the main aspects of British and Spanish colonization that made them similar and the main aspects that made them different. I would mention the following:

Similarities

1. Both set up plantation systems for economic gain: the Spanish in the Carribean and South America, the British in the Caribbean

2. Both were major colonizers that subjugated many peoples and conquered large areas

Differences

1. Time period: Spain was one of the earliest colonizers, while Britian was a little late to the scene. In fact, a naval battle between Spain and Britain in the 1500's marked the end of Spain's heyday as a major colonizer and the beginning of Britain's golden age.

2. Though British colonizers also sent up a plantation system on the Caribbean islands, the system that they set up in the North American mainland was quite different. British colonists on the mainland enjoyed a fair degree of autonomy as farmers, merchants, or craftsmen. 

3. Assimilation with Native Americans: Spanish interaction with the Native Americans they conquered was far greater than British interaction with Native Americans. The Spanish wed and had children with the Native Americans, and introduced many elements of their culture into Native American culture. The British, on the other hand, did not mix nearly as well with the Native Americans, and the British colonists and the Native Americans remained segregated from one another and hostile to one another.