An infusion is simply a "tea". Every time you brew up a cup of Earl Gray, you are making an infusion. The act of pouring hot water over plant material makes an infusion. The stronger you desire the infusion, the more plant material you need to use and/or the longer you need to let it steep, just like when you are making tea! A decoction is a also a tea, just a more potent one. Decoctions are used for densely fibrous herbs, barks, and roots, because they can "cook" longer. In doing so, they release their beneficial ingredients into the water, yielding a more concentrated extraction of the active ingredients.
So, aside from wanting a nice cup of chamomile tea before bedtime, when would you want ,or need, to make an infusion or a decoction? If you are into using herbal remedies, you will often need to make infusions, either to drink, or to use in a poultice. Most decoctions, while not used for drinking, are frequently used in poultices.
Aside from this instance, if you make your own soaps, balms, lotions etc., infusions are a great way to incorporate the healing properties of herbs, plants, spices, and/or shrubs into your product(s). While essential oils will certainly add (much) desired properties, infusions can accomplish the same end result in a (much) less costly manner. In fact, I would venture to say that there are times when an infusion would be a more appropriate choice than the essential oil (EO), especially with regard to infant/child products.
So how do you do it? To make a fairly strong infusion, take 1/4 of a cup of the dried herb, or herb mix, of your choice, and cover with one cup of boiling water. Then cover the pot, so that the vapors will be held inside while it steeps. Leave this sit for at least 30 minutes, then strain it, and either drink it, or pour it into a dark bottle. This is really a make it as you need it thing, and it should be used either that same day, or the next. Putting it in the refrigerator will help if you wish to keep it another day.
For some products, and in certain poultices, making an oil-based infusion is preferable to using a water-based one. You can accomplish this in much the same manner as you do the tea, except that you will not want to boil the oil. Different oils have different burning temperatures, so, while I can't give you a specific degree to heat the oil to, it is only necessary to slightly warm the oil. If you are using a microwave to heat oils, make sure that you only heat in short, 30 second, bursts, and that you exercise extreme caution. Hot oil can cause severe burns.
Put your choice of plant material down into a jar, but before you add the warm oil, take a pestle or a spoon and lightly bruise the plant material. This slight maceration of the plant will help to initiate the infusion process. If you are making a poultice, follow that specific recipe's instruction for the amounts, but if you are making it for use in your own products, you can achieve a fairly concentrated infusion by using three cups of plant material in about 1/2 to 3/4 cup of (your choice of) oil. In either case, make sure that the oil completely covers the plant material, increasing the oil if necessary. Once you are sure you have enough oil to fully cover the plant material, cap the jar tightly and shake it for minute or two. Put the jar somewhere that is dark and cool to steep. It should not go into the fridge, at this point.
For one month, once a day, you will need to take the jar out and give it a good shake for a minute or two. When you are finished infusing, strain the solids from the oil. Since these aren't good for anything, throw them away and bottle the oil. Store the (infused) oil out of direct sunlight, in a cool place. While refrigeration is not mandatory, it is acceptable, and in some instances, even preferred.. Depending upon the oil your chose, it should remain good for a year to a year and a half. Because of the strength of this infusion, you can further dilute it with more carrier oil, and still retain the beneficial properties of the plant material.
Of course, if you don't have a month to wait, you can infuse an oil in significantly less time, however it won't have the same strength, and it will need to be used without being diluted. Since it is difficult to estimate the quantity of properties being infused into the plant material, over what period of time, I suggest that you leave the infusion to steep for at least a full day, preferably two.