They don't need much veg - mine just have a couple inches of carrot, half a big leaf of spring greens and a small knob of brocolli every day - it's best to keep to the same veg and feed daily, rather than changing it about.
By 'introduce slowly' is meant over 2 weeks on one type of veg, going from a mouthful to full portion - if you rush it you just make it slower in the end as it upsets their tums.