In writing, there are two kinds of transitions we need to concern ourselves with. We must be sure that the transition is smooth from one sentence to the next. And we must also be sure that transition is smooth from one paragraph to the next. The strategies for each are a bit different.
When making an appropriate transition from one sentence to the next, we use words and phrases that rely largely on logic. When we present an idea and wish to present a similar or related idea, for example, we use words such as "additionally," "furthermore," or "similarly." If we present an idea and then want to write about an idea that is different, an exception or a contradiction, we use words and phrases such as "on the other hand," "conversely," "but" or "however". The writer does need to focus on whether or not the transitional word or phrase used is appropriate because otherwise it is not going to make sense at all to the reader. Let me give you an example of this:
I am really looking forward to this party because it is going to be so much fun. On the other hand, I expect to get there early to have even a better time.
You can see that using "on the other hand" makes no sense because what I have to say supports what I said before. It does not contradict it. In order to provide an appropriate transition, you must understand what these words and phrases mean logically.
To provide an appropriate transition from one paragraph to the next, the strategy I often use is to end a paragraph with a sentence that talks about the topic of the paragraph I am in and that also mentions the topic of the next paragraph. This creates a little bridge for the reader to walk over from one paragraph to the next and from one topic to the next. For example, if I were writing a paper on being fit, I might have one paragraph on diet and the next on exercise. I could end my paragraph on diet with a sentence like this:
Diet is central to being fit, but exercise is quite important, too.
I have now wrapped up my paragraph on diet, and I have introduced the topic of the next paragraph, which makes a smooth and appropriate transition for the reader.
After you begin to practice your transitions skills, you will see that they become easier and easier to use. Remember that logic is important to move from one sentence to the next and that the reader who gets a wrap up and in introduction to the next topic will be happy with how smooth the transition is.