Obviously, never collect anywhere without (a) a permit from the appropriate authorities in the country in question, AND (b) permission from the person or people who own or control the land.

(1) Identifying Agathis

Agathis is an extraordinarily distinct genus. Two easy vegetative field characters alone suffice to differentiate members of the genus from all other living organisms. These are

(i) the completely flat leaves with parallel resin canals and (obviously) no venation.
(ii) the rounded, ball-like appearance of the growing tips.

Character (i) separates the genera Nageia (Podocarpaceae) and Agathis from all others. Character (ii) separates Agathis from Nageia (which like all other Podocarpaceae has pointy growing tips). If the plant has recently flushed with new growth, it may be difficult to tell the genera apart at first, so a further useful tip is to take a mature leaf and attenpt to fold it so that apex and base meet, and then smooth it with your fingers from the apex/base end to the fold. Coriaceous Agathis leaves will almost always snap. Nageia leaves, which tend to be a bit thinner and more supple, will only seldom snap.

The bark is also extraordinarily distinctive (see picture in Flora Malesiana I: 10 (3): 432), and with experience can usually be spotted from tens of metres away even in dense forest. From above, the trees are often emergent/predominant above the canopy and have a distinctive architecture and appearance. The pollen cones are also completely unmistakeable, but perhaps only to the trained eye, and they are quite difficult to describe.

(2) Collecting Agathis

From a taxonomic point of view, however, it is not the leaves which are important (although if they can be collected they should be) but the male cones. In the Araucariaceae, mature female cones shatter in the canopy, so the taxonomy of the genus is based almost entirely on characters of the pollen cone and the constituent microsporophylls. Shortly after anthesis, these are abscised and fall to the floor, where they often persist for many months in the thick and slow-rotting carpet of Agathis leaves. They are very much worth collecting. Have a look at the photos on the 'Images' page for an idea of what they look like. Spotting them in the leaflitter may be quite difficult at first, but a quick rummage at the very base of the tree usually recovers at least a few. They may well be partially rotted or disintegrated - obviously, if you can collect whole pollen cones they are much preferable, but if you can't see any that aren't damaged don't worry - partially damaged collections are still useful for microsporophyll characters.

I've tried spirit collection, and I've tried drying, and contrary to my fears dries pollen cones, although they do disintegrate, do not do so rapidly. I therefore think drying is preferable, and much more convenient as well. I recommend collection into thick paper bags (I use manila-paper brown envelopes from stationers for this purpose), folding the top over and sealing with a paperclip, and leaving them somewhere warm to dry the moisture from them before sending them home.