Giving decent talks and writing readable papers is a hard task, even for experienced scientists. How do young inexperienced scientists (especially students and new postdocs) acquire these skills? They are crucial to survival in science.
A key component is practice... practice ... practice, especially when coupled with constructive feedback, from both peers and mentors.
Students and postdocs should take every opportunity they can to give talks whether at group meetings, departmental seminars, or conferences. Giving a practice to a smaller invited friendly audience can be very helpful. Even giving a practice to family members or friends who know nothing about the relevant science can build confidence and smooth the presentation.
Supervisors have a responsibility to provide regular opportunities for students and give constructive feedback. However, if they do not, students should not wait around but create their own private forums and at least give talks to each other.
Similar considerations apply to learning to write papers. Lots of practice is key. Students and postdocs should always write the first draft. This may be not the quickest and most efficient way to produce a paper. But, it is a necessary ingredient in training.