Searching either by multiradical or by SKIP method is usually the quickest. To show a few examples:
着
Multi-radical
Go to Jisho.org (or whatever your preferred character dictionary is) and click on “Radicals” from the menu. Then look for components that appear to be used in this kanji.
For 着, the most obvious component is 目. This may be difficult to recognize at first for a low-resolution image, but it’s something that will become quite easy with time.
To find it in the list of components, try to see how many strokes 目 contains. Depending on how much experience you have with handwriting, it may not be always be obvious how many strokes a component has, so you may want to check a range of possible values. For example, 目 has five strokes, but at first glance it may look like six.
Once you’ve selected the component, you’ll be shown a list of kanji that contain it, ordered by stroke count.
Sometimes, it’s easiest just to count the full number of strokes in the kanji and go to that number to see if you recognize the kanji.
In this case, the kanji has 12 strokes, and there are about 33 kanji listed with that stroke count.
If you’re having trouble counting the number of strokes, or if there are just too many options, you can try identifying additional components, such as 羊 (or 丷 and 王) and ノ.
In this case, adding 丷 narrows down the options by a lot, and adding 王 leaves only the correct kanji.
Learning to recognize the radicals and count strokes takes time and a fair amount of trial and error, but it becomes second nature after a while 
By SKIP method
The SKIP method is a bit trickier, but can be very efficient when a kanji has an easily recognized structure.
The SKIP method breaks a kanji into just two parts, arranged in a certain pattern.
For example:
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状 consists of the components 丬 and 犬 arranged in a left-right pattern - ⿰丬犬
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空 consists of the components 穴 and 工 in an up-down pattern - ⿱穴工
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医 consists of 匚 and 矢 in an enclosure pattern - ⿷匚矢
着 is perhaps not the best example, because it’s not really obvious if it is up-down or enclosure.
As it turns out, it is an enclosure pattern, so you go to a SKIP search dictionary (such as Find kanji by SKIP code) and select the icon that looks like a box in a box.
Next, you select the stroke count of the two components: 7 and 5. Many electronic dictionaries also allow you to set an error margin, in case you’re not 100% certain how many strokes there are.
No error margin:
+/- 1 stroke in each component:
Again, this may seem a bit overwhelming at first, but after a while you start to develop a gut feeling that “Oh, this kanji should be easy to find by SKIP method” or “Ugh, this one has so many little details; I’ll just use multiradical”.
Also, some search engines work as a sort of middle ground between SKIP and multiradical, in that you start by selecting a pattern, then select the first component, and then finally the full kanji.
For example, in the screenshot below, I’ve used the iPhone app imiwa. I started by selecting the enclosure pattern, and then scrolled down to enclosing radicals with 7 strokes. Once I’ve chosen the right top part (the one that looks almost like ⺶), I’ll be given a choice between 差 and 着.
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