There is no trick

    I mean it. There is no magic way to convert measurements. The most used 'quick' conversion systems involve doing multiplication and/or divisions in your head, but that is not very practical, especially when dealing with large numbers.
   
   I came up with a different system, and then discovered that quite a lot of people used it. And I mean 'used' as in 'used to', because it happened to myself and other people that I talked to, if you use this trick for long enough, you will probably learn to use the different measurements systems 'natively', without having to 'translate' them to the measurements you grew up with.
   
   But as I said right from the start, there is no trick. It's about memorizing. And no, I'm not telling you to memorize the whole conversion table, that would be crazy. You only need to memorize some "reference points".

   The theory

   Anyone can convert 10 miles to 16 kilometers in his head, right?
   I bet you know that 100km are 62 miles, right?
   Now stop and think just one moment: did you actually multiply 10x1.6 to get 10 miles = 16 km? Did you really calculate 100x0.62? to get 100km=62mi?
   Exactly. You just know those 2 particular conversions, because you have heard them so many times and have memorized them.
   
   Now quick: how many km in 5 miles?
   How did you do that? Kinda like 16:2, right?
    I mean, if you know by heart that there are 16km in 10 miles you also know that there are 8km in 5 miles and 32km in 20 miles.
   That's the whole trick. It's about memorizing some 'reference points', and use those 'known' values to perform quick additions and subtractions, which are much easier to do in your head compared to multiplications.

   It's actually about names

   Think about measurements as "names". For instance, "250 miles" is just another way to say "400 kilometers". Different "names" for the same "thing", in this case a distance. memorize "both names" (metric and imperial) for a bunch of arbitrary distances, and you're done. Next time you have to convert, just pick the closest "known conversion" that you know, add or subtract a smaller one to get even closer, and if necessary "stretch" the result to make it "kind of fit" (you don't really need to know if it's 205 or 195, knowing that is't around 200 is enough)

   Let's try this

   Step one, memorize the different names some "known points": if you know by heart that 6000m and 20000ft are the same altitude, it doesnt matter what you call that altitude any more. If you know that "this high" can be called 3000m or 10000ft, measurements systems don't really matter.
   Next step is to refer to the closest "known point". If you know that 5000m are 16500ft and 6000m are about 20000ft, you don't need to convert to know how many feet 5400m are: you know that is somewhere around half way between 16500 and 20000, and that's more than enough, you don't need to figure out the value.
   
   Still with me? Now for the fun part: when you get really used to do this you suddenly realize that you don't need to convert to your favorite measurements system any more. Seriously. It works. Worked for me, anyway. I started with those quick conversions as explained above, and ended up being able to "think" in metric or imperial measurements without having to convert. I guess that's what happens, provided that you use this "reference points" system long enough.

   Some of my 'reference points'

   What follows is a series of "known conversions" that I know by heart. Just pulling off the top of my head. If you memorize these values you should be able to do quick conversions in your head, not really accurate to the last digit but good enough for the purpose of "knowing what kind of speed" (distance, altitude) we are talking about.
   
   400km = 250mi
   100mi = 160km
   8 km = 5 mi
   125mi = 200km
   200mi = 320km
   800km = 500mi
   
   1000m = 3300ft
   10,000ft = 3000m
   30,000ft = 9000m
   10,000m = 33,000ft
   5000m = 16,500ft
   6000m = 20,000ft
   
   That's it. Memorize those and you will be able to do quick conversions... except when knots are involved.

   Knots make more sense than miles

   Knots are nautical miles per hour and nautical miles are somewhat longer than 'regular' (statute) miles.
   Nautical miles are not arbitrary, they are actual measurements of the Earth's circumference.
    The length of a nautical mile is 1852 (actually, 1852 point something) meters or about 1.12mi, and the geometrical/geographic/astronomical reason why it's exactly that long is that a nautical mile is one prime of one degree of the Earth circumference at the poles.
   
   In other words, draw a line all around the Earth in a circle, and make it touch both the South and the North pole. That's a Meridian.
   Now, divide our circle in 360 degrees.
   Now take one of those degrees and divide it in 60 parts, called 'minutes' or 'primes'. Measure, and you'll find that each 1/60 of a meridian degree is just a little bit longer than 1852 meters, or a nautical mile .
   
   And yes, you are supposed to know this stuff. Didnt you want to be a pilot? :P

   Converting nautical miles

   We usually need to convert only one way, that is to figure out how many mph opr kph there are in this many knots.
   For every 100 knots, add 15 to get statute miles. The actual value is closer to 13 but 15 is easier to handle when having to do quick calculations, and the inaccuracy isnt so big anyway (thanks god we dont need really accurate conversions)
   So, 100 knots are 115mph, 200knots are 230mph, and 150knots are about 180mph.
   Yes, it would be easier if you memorized some values like we did for miles vs kilometers. I never got around that because I dont really convert knots, I just think as them as "slightly longer miles" so if I'm doing 120 knots I know that I must be doing something like 135 or 140 mph but I dont really botehr to find out. That comes with the package. Once you learned to use both miles and kilometers without converting, you also use knots the same way.
   Anyhow, if you use lots of planes that measure in knots, you may want to memorize some reference points as described in the first couple of sections, making it knots vs mph or knots vs kph according to what is your 'native' measurement system