Have you primed the pump by holding the fuel tank above the heater? Also make sure your battery is in good nick, especially for starting. I got my Wallas PCB repaired by this chap but my heater was completely dead beforehand.
You don't say what model Wallas you have, but assuming it's electronically started (via a PCB) you do, as pickledpig says, need to ensure that your battery voltage/condition is in first class condition as the average unit uses around 5 amps to start.
Do check that you have sufficient fuel in the tank AND that you allow several minutes at least for the fuel pump to draw enough fuel to the burner if the heater hasn't been used for a long time.
If you are seeing 'steam' it appears that the glow plug is operating correctly and that the heater is trying to start. As a guide, if we haven't used our heater for several weeks, it can take 5 - 8 minutes before the fans speed up and it starts producing proper heat as opposed to the slow fanspeed start-up cycle.
If we use the heater say once a week, then it's up and away within about three minutes. A lot depends on the distance and position of your fuel tank. Low down and several feet away from the heater means a longer period before the fuel pump, sucking a tiny amount at each 'click', gets the fuel to the heater coil allowing the thing fire up.
So try it several times, each for several minutes before getting the screrwdrivers out!!
Should also have added that you must ensure that the 'push down and twist-to-lock' flue outlet cap is fully open. I got in a real state a few years ago when the damned thing wouldn't start properly. "Steam' was showing out of the flue above deck and I assumed the cap was fully open. It wasn't, but allowed just enough air flow to fool me.
Opened it fully, the heater sort of sighed at my stupidity, then started immediately!!
If there is steam issuing form the heater exhuast as you say and not vapourised parafin then I would guess water has got into the heater, probably through the exhaust. If this is the case it will be a complete strip down job and may require part replacement.
However, if it is parafin vapour, the wick probably needs cleaning and adjusting, which means it still needs to be taken apart. It is quite easy to get Wallas heaters apart but it is like building a playing card castle to get them together again. Also be aware there is a tiny rubbery reset button immediately above the upper hot air outlet. its always worth a press if the heater doesn't start.