Play it early on
It is essential in fantasy football to be near the top of your league early on as it becomes increasingly hard to make up ground on the opposition as the season unfolds. Teams tend to converge and often employ 5-8 players that seem to be present on most teams (see Ronaldo, Lampard, Gerrard, Vidic, Bosingwa and Schwarzer in 2008-09). It therefore makes sense to get your team right early on before it is too late.
A further advantage to playing your wildcard early on is that you can buy the hot players now before their price rises too much. Assuming your team is currently still worth 100m, you will be able to buy more for your money now than in 3 months time.
The disadvantage of course is that if you pickup injuries or your players lose form later in the season it will take you several weeks (or alot of points) to rectify the situation.
Play it when the injuries start to mount up
So far, not too many fantasy quality players have been injured, with Modric and Fabregas the only big names to pick up injuries so far (though the likes of Ferdinand, Zhirkov, Santa Cruz and Arteta have yet to feature for their respective teams). It is inevitable that some injuries will come and it is useful to have your wild card stashed away to rescue you in this situation.
The Champions League starts on 15 September, with the group stages running until 09 December. This is prime territory for injuries and rotations so the wildcard might be well played during this period. This is definitely the safest option and the one that will likely be used by most players.
Save the wildcard for a late season push
If your team is in contention by, say, week 25, the ability to repick your team and get all the form players could tip the league in your favor. You will be able to ride teams with something to play for and avoid those who are just playing the season out. For example, right now we would consider Villa defenders a fairly poor choice but come February when the new signings have settled in and the team might be pushing for Europe, they could be a great option.
The risk here is that your team is so far behind and that teams all look so similar that the wildcard's value is diminished.
The more I think about it, the more I think that playing your wildcard early on is the way to go. I'm not saying pull the trigger in week 5 if your team is okay but if you get a couple of injuries over the international break and a couple of your squad players aren't panning out then using your wildcard to get players such as Shawcross, Lennon or Adebayor will be beneficial before their price rises further. I am aiming to use mine in approximately week 8-10 when we have a good idea of how teams are shaping up after the transfer window, as well as the rotation consequences of the champions league.
Remember, when you do decide to play the wildcard, especially if you take this decision early, you must make long term decisions and not be too concerned with a favourable game that week. Many get overly concerned with double gameweeks and easy matchups and therefore make short term decisions which cripple their flexibility for the future. Good luck making this important call and let me know how your cards fall.