[*Edited after comments and additional research.*]

**Aerobic training will not prepare you for altitude**

Some of the answers here are misleading. According to the Altitude Research Centre: 

> Being physically fit does not prevent you from experiencing AMS (Acute Mountain Sickness)
> symptoms. There does not seem to be a link between fitness level and
> susceptibility to altitude illness.

**Altitude sickness is a significant risk at 14,000 feet (4,200m)**

At 14,000' (4,200m) you're only getting 60% of the oxygen at sea level. Altitude medics classify 14k as "Very High Altitude" which is a strong hint that the dangers are significant.

Susceptibility to AMS appears to be genetic and varies widely between individuals. Estimates of incidence levels are all over the place in the literature, but we can safely say that a significant percentage will experience quite severe physical and cognitive issues if they ascend rapidly to 14k.

Don't underestimate the impact. Even mild AMS is extremely unpleasant and can affect your ability to move safely on technical ground. Severe symptoms can be pretty much paralysing. I'm very susceptible to AMS and know this from experience.

So it's important to follow the [Golden Rules][1] and not push on if you experience symptoms. Rapid descent will always resolve early symptoms - the problem is that denial is extremely common as people are keen to reach their goal and not disrupt the rest of the party. This is how the serious issues occur.

Currently, the only way to know your own response to altitude is to suck it and see. So it's important to be cautious on your first high ventures, and pick routes with an easy retreat. Even people with known low susceptibility can suddenly experience problems, so always be prepared to descend if you feel unwell.

**How to acclimatise before ascending to 14,000 feet (4,200m)**

It's very important to distinguish between two scenarios:

 1. The typical alpine trip where you make day-climbs to the peak, but descend to sleep below 8000 feet (2400 meters). That is what we are discussing here.
 2. A trip where you will be progressively sleeping at higher altitudes. This is a whole different ballgame and life-threatening problems are
    quite common. Do your research and understand the proper protocols
    for gaining height.

***Traditional acclimatisation***

The **only** proven way to acclimatise fully is a programme of training climbs at increasing altitudes. If you know you are one of the lucky ones, you can head straight off to your 14 thousander. For the rest of us, you'll need 1-4 days to acclimatise depending on your physiology.

I'm prone to sickness, so personally I find it best to be conservative and climb up to around 9,000' (2,700m) on the first day while sleeping low. Even this can be quite uncomfortable. Then I'll add 1,000' (300m) or so a day if things go OK. If I'm relatively symptom-free on an 12,000' training climb, I'd feel ready for 14,000' (4,200m). If you're less susceptible, you can accelerate the process. Only experience will tell.

***Altitude tents and masks***

This is quite an expensive and disruptive process. The equipment can be hired or purchased if you don't have a suitable facility nearby. [US Army Research][2] suggests that tents are better than nothing, but are far from a full substitute for traditional acclimatisation. For a 14 thousander, it's unlikely that this will be the way to go.

***Medication***

The only recognised medication is Diamox (Acetazolamide).

Diamox is far from risk-free, with [many unpleasant but benign side-effects][3] and occasional [life-threatening reactions][4]. And recent research suggests that it is [not measurably effective][5] for countering the effects of strenuous exercise during rapid ascent.

In the UK, the clinical authorities recommend against using Diamox prophylactically, so you won't get a prescription. It's available in the US, but the risk/reward ratio doesn't look good and you certainly shouldn't rely on it preventing AMS at 14k.

**Take-home points**

 - The dangers of rapid ascent to 14k are significant
 - Only experience will tell you how long you take to acclimatise
 - If you do need acclimatisation, the only proven approach is traditional training climbs
 - Tents and masks only provide modest benefits, while medication has significant side-effects and may well not work in this scenario.

  [1]: http://www.ismm.org/index.php/the-golden-rules.html
  [2]: http://www.outsideonline.com/1784286/do-altitude-tents-work
  [3]: https://www.drugs.com/sfx/diamox-side-effects.html
  [4]: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3743627/
  [5]: http://online.liebertpub.com/doi/abs/10.1089/ham.2010.1003?src=recsys&