I have met a lot people now who are traveling on a shoestring budget, these are the tips I have picked up for New Zealand (most are generic to any country).
Flights– this is going to be a big cost, I don’t know a way around it, sorry. It can be reduced by using Apps like skyscanner to find the cheapest flight.
Travel– A few options here: hitchhike; New Zealanders are very good at stopping for travelers. Rent a car; this can later reduce accommodation and activity costs. Bus; intercity is the big company but manabus is often cheaper (look at different days/times as the prices vary considerably).
Accommodation– A few options here: take a tent and camp. If you have a car sleep in it-also for a small cost some hostels let you park and use their facilities. Hostels, especially dorm rooms are pretty cheap- top tip here would be to look at discount cards like BBH (the discounts soon add up). Another option for Hostels is to see if they have work to stay e.g. you clean etc in the morning to stay at the hostel for free.
Food– Unless you really want to eat out cook at the hostel or a portable stove if camping. If you are staying in Hostels its worth checking out the free foods (food left by guests-if you don’t take it someone else will) before going shopping. Also go to supermarkets near closing to get reduced foods.
Activities– The great thing about New Zealand is so much is free (you just need to get there), my articles on the places I visited will have everything I did for free. For activities that aren’t free, before booking look at bookme and ask the hostel if they have a discount.
Last tip– Check out visa options and if possible get a working visa so if you are short on cash you can try and get some work.