A famous naturalist once said, "Without a hypothesis, a geologist might as well go into a gravel pit and count the stones."
A hypothesis is a "tentative proposition which is subject to verification through subsequent investigation....In many cases hypothese are hunches that the researcher has about the existence of relationships between variables." (Verma and Beard, 1981)
The hypothesis is the cornerstone of science, and hypotheses can be constructed and used in different ways.
In studies of complex, multi-factor systems (e.g., ecology and evolution), a hypothetico-deductive approach is often taken. On other areas, such as cellular and molecular biology, developmental biology, and other areas, hypotheses may be reached inductively, and a set of competing hypotheses potentially able to explain a given observed phenomenon may be tested and systematically eliminated until only the most likely explanations remain. To better understand each method, we should first review the differences between inductive and deductive reasoning.
Inductive Reasoning is sometimes called the "from the bottom up" approach. When we use inductive reasoning, our specific observations and measurements may begin to show us a general pattern. This might allow us to formulate a tentative hypothesis that can be further explored, and we might finally end up making some general conclusions.

In this case, one might construct an argument such as:
For example:
One potential pitfall here is the "inductive leap": When you make the jump from many specific observations to a general observation, your generalization might not be correct every time.
Although generalizations are certainly useful, the wise investigator is aware that there may be exceptions to a general rule, and even to the possibility that the "general rule" might eventually be found to be wrong more often than not.
Deductive Reasoning is sometimes called the "from the top down" approach. In this case, we start with a general idea and work down to the more specific.

Deductive reasoning is used to test existing theories and hypotheses (general ideas) by collecting experimental observations (specific examples) that put those ideas to the test. One of the most useful ways to use this method is to construct a syllogism, a specific type of argument that has three simple steps:
For example:
The results of your study may suggest further experiments. (What types of hymenopterans don't have stingers? Which is the primitive condition: stinger or no stinger? Why has stinglessness persisted?)
Important aspects of the hypothesis...
The Theory
Example: The theory of evolution by means of natural selection.
The Law
Example: The Laws of Thermodynamics
German philosopher Karl Popper wrote in his famous essay, Science as Falsification, that it is vulnerability to falsification--not repeated verification--that is the hallmark of truly powerful hypothesis.
2. Before you begin, arm yourself with predictions about what you think will happen if you test the hypothesis.
3. Design careful, rigorous experiments to put each hypothesis to the test.
4. Carefully analyze the results.
5. Decide whether the results support or refute the hypothesis you are testing.
6. If you have multiple hypotheses, this process continues until one hypothesis is the "last man standing".
7. The hypotheses that are not falsified by experimental testing are provisionally accepted as potential explanations for the observation.
Ridiculously simple example:

In the example above, it's easy to see that dipping a net into the ocean isn't a very high-tech way to address this problem. But with more advanced technology such as

You might well be able to refute the "no fish" hypothesis. Science marches on as technology improves.
If you're into metaphors, you might compare hypotheses constructed to Popperian standards to be like a castle or fortress...

It may look well built from the outside, and seem to be perfectly sound. You may be able to add more blocks and mortar (analogous to finding evidence that appears to support your hypothesis: each dip of the net "confirmed" that there are no fish in the Pacific Ocean, right?)
but until you test the "castle" by actually attacking it...

...you don't really know how strong it is. If it wasn't well constructed, it may end up looking something like this:

For example, if you want to know whether a new drug actually helps people quit smoking, the exploratory phase will involve a statistical question:
"Will smokers taking SmokeAwaytm have a higher rate of giving up smoking than smokers given an indistinguishable placebo?"
In this method, two muturally exclusive hypotheses are compared
Well-designed and executed experiments will indicate which of these two competing hypotheses should be rejected, and which should be (provisionally) accepted.
Platt wrote:
2. Devising a crucial experiment (or several of them), with alternative possible outcomes, each of which will, as nearly as possible, excludes one or more of the hypotheses;
3. Carrying out the experiment so as to get a clean result;
4. Recycling the procedure, making subhypotheses or sequential hypotheses to refine the possibilities that remain, and so on.
It is like climbing a tree. At the first fork, we choose--or, in this case, "nature" or the experimental outcome chooses--to go to the right branch or the left; at the next fork, to go left or right; and so on. There are similar branch points in a "conditional computer program," where the next move depends on the result of the last calculation. And there is a "conditional inductive tree" or "logical tree" of this kind written out in detail in many first-year chemistry books, in the table of steps for qualitative analysis of an unknown sample, where the student is led through a real problem of consecutive inference: Add reagent A; if you get a red precipitate, it is subgroup alpha and you filter and add reagent B; if not, you add the other reagent. B; and so on.

The Differential Diagnosis scene in every episode of "House" is a bit like a cartoony, quick-n-dirty example of strong inference.

"The process known as the Scientific Method outlines a series of steps for answering questions, but few scientists adhere rigidly to this prescription. Science is a less structured process than most people realize. Like other intellectual activities, the best science is a process of minds that are creative, intuitive, imaginitive, and social. Perhaps science is distinguished by its conviction that natural phenomena, including the processes of life, have natural causes--and by its obsession with evidence. Scientists are generally skeptics." (from Biology by Neil A. Campbell)
The scientific method, requirement of physical evidence, falsification and, especially, WILLINGNESS TO MODIFY OR EVEN REJECT LONG-HELD IDEAS THAT TURN OUT TO BE WRONG are hallmarks of science, and are what sets them apart from religious faith. The two philosophies are entirely different, and should not be taught in the same context.
References
Platt, J. R., 1964, Strong inference. Science 146: 347-353.