The most important transitions come between paragraphs. Try to establish a connection between the first sentence of a new paragraph and the last sentence of the preceding one. Again a linking word may be the easiest way:
. . . Thus the pattern established by Dickens in the first chapter is consistent throughout the rest of the first volume.
However, Volume Two offers a new approach to the narrative. . .
The echo of a key phrase or word can also be effective:
. . . Whatever Lear's faults, it cannot be denied that he loves his daughters.
Unfortunately, love counts for little in the realm of Regan and Goneril. . . .
However, echoing the preceding sentence too closely will result in repetition rather than transition. This example was an attempt to link the introduction to the body of the essay:
. . . The other important function Bottom has is his major contribution to the humorous aspect of the play.
One of the major functions of Bottom is his contribution to the play's humour. . . .
The transition may require more than just a word; a transitional sentence may be called for:
The evidence thus suggests that there is no other option.
And yet there may still be a solution. If you disregard . . .
The transitional sentence does not indicate what will come next in the paragraph, but it establishes that this paragraph is a negation of the last. Note that this kind of sentence displaces the topic sentence you would expect to find at the beginning of the paragraph; the topic sentence should follow it.
Sentences must follow one another in a logical pattern. If thoughts follow one another without sufficient connection, the essay will make no sense. Within each paragraph you will be using transitions almost continuously.