If you're at home, use a floor pump.
They are very easy to use and have a gauge so you can measure the pressure.
When you're on the road, the quickest and easiest way to get you back on the road is to use CO2 cannisters.
They are not that cheap though and the CO2 will leak out of the tube faster than air (mostly N2), requiring topping up over the next few days.
More information is available on Wikipedia
bicycles.stackexchange.com/users/1588/Mac
If you're at home, I recommend an air compressor , there's no easier or quicker way than this.
Usually these have pressure gauges, and you can even (with some accessories you can) control the max.
pressure, just press and
it stops when done.
If on the road, the easiest way (and also the quickest) is: If near a gas station, use their air compressor (if available)
Otherwise, use a portable air solution (the quickest is the CO2, but mind the cost of the refills), there are really nice hand pumps also,not the quickest, but easy IMO.
Finally, and knowing that in my case I just need to inflate every three weeks, I would recommend getting newer inner tubes, maybe the ones you're using are loosing air quicker than normal?
(I mean, inflating every week could be too much, although I understand if you really want them to be tip-top :)
bicycles.stackexchange.com/users/1280/jackJoe
Answer:
Mini-Pump in combination with a Track Pump.
Read on for my experiences of 'Cyclaire' pumps...
I purchased a 'Cyclaire' portable pump as I genuinely believed it would be the answer to all of my puncture/tyre care problems.
It came with a neat bag that I could use to carry it on the bike and worked perfectly.
However, on a day to day basis I carried a mini-pump and over time I forgot to dust off the 'Cyclaire' pump, to eventually never even think about taking it out for longer rides.
If I was on tour with a group
then I might just dig it out as it does have a gauge and high pressures can be achieved.
This could be useful to maintain tyre pressures 2+ weeks in to an 'expedition'.
As it is, I recommend a small plastic mini-pump for the road and a track pump for back home.
The trick with the minipump is to get one where there are no extra gadget features, e.g. gauge, 2-way motion, telescopic barrel or any of that nonsense.
These features can make the pump liable to rattle apart, rendering it useless when you need it.
The simpler (but not necessarily cheaper) pump just keeps on giving.
The portable pump only has to get you home, you can ride on 20 p.s.i.
if that is all the minipump can give, back home
you can then get the rest of it in effortlessly with a gauge to keep it correctly inflated.
Maybe
the 'Cycleaire' strays from 'keep it simple', as does the CO2 cannister.
A workshop compressor is nice, but, unless you work in a bike shop and need one on the whole time, then you have to faff with it and wait for its cylinder to charge.
For that reason, stick with the track pump (with gauge) and plain-as-possible mini-pump for on the road.
If you really want a 'Cyclaire' pump then find a suitable scenario - either the long tour or, if you commute, inside your desk drawer.
bicycles.stackexchange.com/users/1487/ʍǝɥʇɐɯ
Definitely a floor pump (with built-in gauge) for regular at-home inflations.
Fast, accurate, easy, can handle any pressure.
I've never tried the CO2 inflaters
but I assume they work.
Most mini-pumps suck -- too little volume for fat tires and too little pressure for skinny tires --
so for on the road I'd recommend a full-sized frame pump.
bicycles.stackexchange.com/users/1584/Daniel R Hicks
Another Option would be to use the air pumps for the cars by your local gas station.
I really like this option, because the pumps there have enough pressure for most mountain- and citybike tires.
If you have a Schrader valve, the air pumps will connect directly.
If you have a Presta valve, you can use a converter.
It weighs like one gram and will fit anywhere.
Eg, duct tape one to your seat rail.
Also, at least in the city where I live, there are gas stations all around.
Be careful thought, these pumps fill up a bike tire pretty fast!
So if your pass a gas station on your commute, this could be even the fastest option.
bicycles.stackexchange.com/users/1494/Paul Weber
While the question is directly about easiest/fastest way to pump up a tire, it is worth noting that all the above methods work.
It really comes down to fastest.
Try benchmarking against a flat car tire.
This is a high volume, low pressure problem, which while different from a bike tires (low volume, higher pressure) is a good benchmark of speed.
It is actually an interesting challenge to pump a totally flat car tire up with a small frame pump, a floor pump, or a CO2 cart.
Alas, a compressor takes all the fun out of it,
bicycles.stackexchange.com/users/19/geoffc
I find that I need to pump up my tyres at least weekly and am looking for how to make this quick and easy.   So what is the easiest and quickest method of pumping up a bike tyre?  As an example, I found this device recently. (forwarded to the best part)
What is the easiest and quickest way to pump up a tyre?
bicycles.stackexchange.com
<tire><innertube><pump>
bicycles.stackexchange.com/questions/6891
bicycles.stackexchange.com/users/1547/Valamas
The easiest way to pump up a flat tire depends where you are. If you are at home, a floor pump seems to be the best answer. If you are on the road, there are a few options. You can use the compressed air at the nearest gas station, otherwise, use a portable air solution (the quickest is the CO2, but mind the cost of the refills), there are really nice hand pumps also,not the quickest, but easy to use. An additional recommendation is a Mini-Pump in combination with a Track Pump. Some cyclists think the Mini-Pump is not useful because it is small and low-pressure. Practical options include floor pumps and air compressors for home use, and mini pumps, frame pumps, CO2 cannisters and gas station compressors for the road. Air compressors at home can take time to charge, while mini pumps can be awkward, especially when they have extra features. CO2 pump refills can be expensive, but they are quicker. Frequent need for inflation could indicate a slow puncture.
Practical options include floor pumps and air compressors for home use, and mini pumps, frame pumps, CO2 cannisters and gas station compressors for the road. Air compressors at home can take time to charge, while mini pumps can be awkward, especially when they have extra features. CO2 pump refills can be expensive, but they are quicker. If you have to inflate your tyres often, maybe you have a slow puncture and should replace the tubes.