Training involes providing support for stems to ensure maximum display. It is necessary for climbing houseplants, houseplants with long and weak stems, houseplants which bear heavy flower-heads and for houseplants whose stems are brittle. Training needs to be done while the growth is still young, fresh and flexible to avoid causing damage to the plant. The support can be provided in different ways depending on availability and personal preferences as well as the houseplant concerned. Some of the common types of support are the well-known moss-stick, trellis, canes, climbing frames among others.
Do not tie stems too tightly to the support. Train new growth before it becomes too difficult to bend. Frequently train plants with tendrils like vines to prevent the tendrils from tying the stems together.
You could leave a few untrained shoots hanged down from a climber; it can improve its appearance. However, this is a matter of personal judgement and preference.
For specific houseplant requirements, look it up in this Houseplants A-Z Guide.