As with most things in our world, the process of identifying insects is largely based on simple observation. The process essentially involves the observer going about collecting the information, reviewing said information - perhaps comparing it to other field notes - and, finally, delivering a "verdict". Of course one of the major prerequisites of observing insects is an inherent respect for what they do within our ecosystem. With this respect, you can go about appreciating the finer points of an insect's existence.
If you are an "insect hunter" - someone out to enjoy and observe the interesting habits of insects - there are three basic research items to consider about your subject:
Habitat: Pay close attention to the environment of your specific insect. If you are looking for a certain type of insect, understand where you may find them in nature. For example, gardens are a tremendous source to finding many active species of spider, butterfly, bee and beetle. Open fields are another great source, especially for crickets as well as spiders. Forests and marshy locales attract specialized species requiring these facilities - bodies of water tend to be a good source of mosquitoes and dragonfly. Of course showcase extra special care when attempting to locate an insect source in and around areas of rubble or refuse as these environments are highly unpredictable (you might accidentally disturb an ornery (and poisonous) Brown Recluse spider or hidden bee/wasp hive. Simply put, always be on your guard!
Time of Day: For a good portion of the insect kingdom, activity will usually peak around midday, typically when the temperature is at its highest (especially true for bees and butterflies). Some insects will become more active at dawn or dusk (such as mosquitoes) but most are busiest at night (spiders and moths).
Equipment (Optional): Carrying a magnifying glass or digital camera/camera phone is a good idea if possible. Such instruments allow for careful up-close observation to really allow the observer to see details often missed through viewing with the naked eye. A digital snapshot of the insect can be further dissected in the comfort of your home at a later time. Also consider carrying a notebook/sketchbook to jot down descriptions and observations while completing the occasional sketch or two. Finally, purchase or borrow one of the many available field guides to allow for quick look-up of a species in question (similarly, consider utilizing this very website on your tablet or smartphone in-the-field). Though all of these items are quite optional, having them in your care takes your insect identifying skills to the next level - resulting in a new level of appreciation for these mighty creatures.
With all that said, here are a few questions to ask yourself when attempting to identify an insect that you have been observing - either outdoors or indoors (an Insect Dichotomous Key will assist you in the same way):
How many legs does my insect have?
If the answer is six legs, you are most likely looking at an insect. If your answer is eight legs, you are most likely looking at a spider.
Does my insect have any wings?
The answer to this question will tell you if it is a walking insect or a flying insect. Some insects do have wings but these prove unsuitable for flying, especially over long distances. As such, the insect may resort to hopping about
Does the insect have any noticeable antennae or feeler appendages?
If so, do they end in a point or are they 'knotted' at their ends?
Are there any noticeable moving jaw (mandibles) or mouthparts?
This will tell you much about the types of food the insect may eat. Spiders will usually have biting pincer-like mouth parts whereas a butterfly will have a straw-like mouth appendage for sucking nectar from flowers.
Taking these items into consideration - and coupling them with honed observation techniques and an accurate insect resources (field guide) - one can begin to discern the varied amounts of insect species in our world. When one finally gains a respect for these creatures, they will open their eyes to a brand new world that exists beyond our own comfortable lives.