Even if you get yourself very fit before going to altitude you may still get into trouble if you go too high too soon. If you fly out to Lukla you will already be over 11,000 feet and so will be more vulnerable to altitude sickness than trekkers who have enough time to take the old tradition route by travelling by road to Jiri and then walking up to Lukla.
Two of the most vulnerable types of trekkers are the young super fit ones who think that they know best and organised group trekkers who must keep to a predetermined schedule. A group can only travel at the speed of the slowest member and so there is a tendendency for the less able trekker to hide any symptoms as they do not want to let the side down.
The hospital at Kunde near Namche Bazaar deals with many trekkers suffering from the effects of altitude. When I was there in 1999 the doctor there told me that a young porter almost died earlier that year due to the effects of altitude and exhaustion from carrying too much trekkers gear too quickly.
The likeliness of contracting altitude sickness can be minimised by controlling your rate of ascent. Kala Pattar and Everest Base Camp are around 7000 feet higher than Lukla. A sensible rate of ascent of around 1000 feet per day with a rest day of 1 day per 3000 feet suggests a minimum of 9 days to get from Lukla to Everest Base Camp. Ascending more than 100 feet a day is alright, the 1000 feet is measured from one camp site to the next. This means that depending on how you feel on the designated "rest" day you can either hang around or take a days hike and return to the same camp site. On the route to Everest Base Camp most people stay in Namche for two nights, maybe taking a hike around Khumjung and Kunde or up the valley towards Thame on the rest day. Others stay in Namche and soak up the atmosphere, thats what I did!
Temperatures can soar during that day and it is very important to ensure that you do not get dehydrated. Bottled water is available along the popular routes but can get expensive as you really need to drink at least 6 pints of liquid a day. If you are camping boil some water and fill you water bottles with it just before going to sleep. This way you will have hot water bottles at night and a good supply ready for the next morning.
Some publications suggest taking the drug Diamox with you. I tried to get some but was told that it is not available over the counter in the U.K. Our trek leaders said that the best way of combating altitude sickness is to be aware of the symptoms and to descend to a lower altitude and take a rest day before re-ascending.
Most people travelling up from Lukla will experience mild symptoms of altitude sickness, just listen to your body and take the appropriate action.
Some of the symptoms of altitude sickness are :-
Make sure that you drink enough water and wear snow glasses all the time, that way you will know that and persistant headache will be due to altitude rather that heat exhaustion or snow blindness.
Appendix C of Jamie McGuinness' book Trekking in the Everest Region is an excellant synopsis of health problems in particular Altitude Sickness, make sure you are prepared!