If details of plant height are carefully recorded on the label, you may well not need the whole stem to be present. Care should be taken not to just collect the upper part without reference to basal (radical) leaves, as well as lower and middle (cauline) leaves. If necessary, multiple sheets should be used and labelled accordingly (Sheet 1 of 2; sheet 2 of 2, etc.) Loose parts such as flowers or fruit can be placed in separate folded pockets and attached later to the sheet. Where possible, the underground parts of the plant should also be collected (though remember in Great Britain, it is unlawful to uproot plants without the permission of the owner of the land).
Rare species should not be collected, but instead photographed and notes taken, annotated with drawings as appropriate. For full lists of protected species in the British Isles, see under Conservation considerations.
Traditionally, plants were collected and placed in a vasculum in the field to keep them from wilting until being placed in a press (The vasculum was lined with wet paper). The plastic bag has universally replaced the vasculum, but care needs to be taken to protect from the sun.
If a press (or a cardboard folder tied with string – called a carpeta by Spaniards) can be taken into the field, then the final results are much better and subjects like poppies even retain their petals. Species of poppies (Papaveraceae), sun and rock roses (Cistaceae) are especially difficult, losing their petals very easily.
It is a good idea to label bags carefully so as to remember which specimen came from where.
The late Professor Peter H. Davis of the University of Edinburgh, published an amusing article called Hints for Hard-pressed Collectors available here as a download with permission of the Editor of Watsonia, the Journal of The Botanical Society of the British Isles.Hints for Hard-pressed Collectors (Adobe PDF, 7 pages, 135KB)
Although dated, the article contains many good ideas from a very experienced field botanist.