Also, you can check out the free guide on eNotes called, How to Write a Character Analysis.

What you are concerned about is transitions in your writing.  There are many ways to accomplish smooth transitions from one sentence to the next or from one paragraph to the next. 

The first thing you should pay attention to is the connections between sentences.  You can ask yourself whether each statement you make is related to the statement before.  For example, if I say, "People are worried about a swine flu epidemic," then my next sentence should be connected to that idea.  If it isn't, then you are not on the right track!

We use many little words and phrases to connect one idea to another idea.  Some of the transitional words we use are logical connectors, like "but," "however," or "nevertheless."  We use other kinds of connectors, such as "for example," or "for instance" to show the reader that an example is coming.  We can also use words like "first" and "second" to show the order of our ideas or examples. 

When you are trying to connect one paragraph to the next, you can use what I call the "old/new" principle.  That means ending a paragraph with a sentence about that paragraph and about the topic of the next paragraph.  That helps the reader move from the idea in one paragraph to a new idea in the next paragraph. 

I have provided a link to a website that will give you more examples of transitional words and phrases.  Good luck!