Transitions are like bridges between the parts of your paper.  They are cues that help the reader to interpret ideas in the way that you as the writer want them to be interpreted.  Transitions help you carry over a thought from one sentence to another, or from one paragraph to another, and link your sentences and paragraphs together smoothly so there are no abrupt jumps or breaks between them.  Here is a list of common transitional devices and how they are used:

To add: and, again, and then, besides, equally important, finally, further, furthermore, nor, too, next, lastly, what's more, also, moreover, in addition, first, second, third, etc.

To compare: whereas, but, yet, on the other hand, however, nevertheless, on the contrary, by comparison, where, compared to, up against, balanced against, vis a vis, but, although, conversely, meanwhile, after all, in contrast

To prove: because, for, since, for the same reason, obviously, evidently, furthermore, moreover, besides, indeed, in fact, in addition, in any case, that is

To show exception: yet, still, however, nevertheless, in spite of, despite, of course, once in a while, sometimes

To show time: immediately, thereafter, soon, after a few hours, finally, then, later, next, then, previously, formerly, first, second, third, etc.

To repeat: in brief, as I have said, as I have noted, as has been noted

To emphasize: definitely, extremely, obviously, in fact, indeed, in any case, absolutely, positively, naturally, surprisingly, always, forever, perennially, eternally, never, emphatically, unquestionably, without a doubt, certainly, undeniably, without reservation

To show sequence: first, second, third, etc., next, then, following this/that, at this time, now, at this point, after, afterward, subsequently, finally, consequently, previously, before this, simultaneously, concurrently, thus, therefore, hence, soon, and then

To give an example: for example, for instance, in this case, in another case, on this occasion, in this situation, take the case of to demonstrate, to illustrate, as an illustration

To summarize or conclude: in brief, on the whole, to sum up, to conclude, in conclusion, as I have shown, as I have said, hence, therefore, accordingly, thus, as a result, consequently, on the whole