Finding a quality specimen to photograph is going to be your biggest challenge, and as already mentioned, be prepared to spend plenty of time looking. Don't expect to go out once and come home with that competition winning photo or you are going to be very disappointed or very lucky.
Take a friend or two with you. Small groups of 2-4 people can search a larger area more thoroughly and improve your chances. Or choose a nearby bush reserve or track and visit it weekly from April to August. Learn where the fungi can be found as many will reappear in the same location each season.
One of the search methods used is to cover a large area very thoroughly. This only works if the forest is reasonably open. The other is to simply follow the walking tracks, searching both sides as you go.
I tend to use both methods. I follow the track till I spot a fungus, then search an area around it. It's surprising how many different fungi will often accrue in the same localised area. Then you don't find any more for another 100 metres or so down the track.
Fungi, like all things in nature, follow the flow of seasons, with autumn being the peak time for fruiting, with a lesser number found during winter. Then another, smaller peek in spring. There are exceptions in poor seasons; there may only be a small peak in autumn and very few fungi throughout winter and spring.
Rainfall and, to some degree, temperature have much to do with fruit body production. In saying this, your geographic location, altitude, and habitat type also have their parts to play. For example, here in New Zealand, in the South Island, where it snows, it's likely to have a very short season. Here in Auckland, the season starts in May and goes through to August. The central plateau (higher altitude) has a very early season, with fungi being found even as early as March.
Fungi species also follow a sequence through the season, with different fungi fruiting at different times. The Russula's are first, often after the first rains of autumn, followed by the Boletus and the Lepiota'si. Later in the season, when it is much wetter and colder, the waxgills can be found. Again, there are no hard and fast rules, or at least none that the fungi will follow. Then there are many fungi that are just plain opportunists, such as Auricularia cornea or Coprinus micaceus which will fruit when conditions suit (plenty of rain) even if it's the middle of summer.
The distribution of fungi is not well understood. I have over the years noticed that some fungi seem to be restricted to not only one particular bush reserve but to small areas within it. You then have to travel a long way or even to another region before finding the same species again.
This may in part be due to very little collecting and identifying that accrues and the loss or fragmentation of native forest habitats. Climate and geographic location also have a part to play.