When you say 'new lawn laid' was this turf or seeded? I'll presume turf as you said 'laid'. It's a shame your suppliers didn't give you aftercare instructions. Regular cutting is what your lawn needs - not too short or you'll scalp it - but regular little and often - at this time of year it should be growing well (particularly after all the rain we've had) so it probably needs mowing twice a week if possible. In the summer lawns should be cut at least once a week minimum.
This link will give you some tips on cutting your lawn http://www.rolawn.co.uk/mowing-your-turf.html
As for the fertiliser - you can use it once every 6 weeks between spring and September, then in the autumn give it a dose of an Autumn lawn feed - this usually contains something that will kill any moss that is establishing in the lawn, as well as a slow acting fertiliser that will work all winter.
Don't worry about not being confident gardeners - we've all had to learn somewhere and we all make mistakes - the friendly lot on here are happy to help each other out so just ask if you're not sure