To add to the good advice above, organizing following a blueprint before writing is extremely helpful.  Then, when writing always use transitional words. Finally, revise your paragraph by rewriting for cohenrence and untiy.

Now, regarding your paragraph, you can combine the first and second sentences in order to make a more interesting and effective topic sentence:

One of the most successful fantasy sitcomes, 3rd Rock from the Sun is a thirty-minute televison show that has run with 139 episodes; presently it can be viewed on weeknights on Channel 20 at 7:30 p.m. EST.

Revise sentences for clarity and organization. For instance, avoid the vague "it."  Here is some of what you have written followed by a revision which can serve as a model for you.

It forecasts a group of aliens trying to pass as ‘typical’ earthlings while living among humans in ordinary suburbia, where they appear zany and occasionally deranged due to their spacey heritage. They become confused and entranced by the commonplace, from everyday things to emotion like love or aggression.

Revision:

This show, which features a group of aliens, who try to pass themselves off as "typical" earthlings living in suburbia, create zany and inconguous situations because of their lack of understanding of earthly ways.  For instance [transition], they become confused, yet entranced by the mundane for earth, and are certainly perplexed by human emotions such as love and aggression.  In one episode the aliens _______________________________[describe what they do as an illustration of your point]

Then, tie your last part better to the previous sentences by connecting ideas.  For instance, write something like this, using transitional words,

Because of the original design and unique, zany humor of 3rd Rock from the Sun, the show has received awards, such as ...., an award received for the episode entitled "Moby Dick," written by ______, an episode which portrayed _________.

For your aid, there is a link below which gives pointers on writing "a perfect paragraph." Also, there are instructions on book reviews, which can be applied to TV show review, as well.

Some good details, but the presentation is unclear. Is this show still in production? If not, you should use past tense and give the dates of its production. The next issue is organization. You start with the broadcast details, then move to plot, then to awards, then to details of a specific episode. You need to organize this more clearly, perhaps starting out with a statement in the form "Title of Episode", directed by Name and written by Name, was the Nth Episode of Season X of "Title of Show". Next, briefly summarize the show, including how many seasons it ran, number of episodes, and major awards.

Next, you need to provide a basic overview of the main characters and plot line of the show as background for discussion of the specific episode.

Also, work with the Writing Centre at your university on syntax and word choice.