This cargo ship departs Tutuila for Ofu and Ta'u every second Thursday morning, and returns Friday mornings. Book in advance: you'll need to call to do so, or ask your accommodation to help out. The journey takes between eight to 12 hours.
Take all of this with a grain of salt. The aging ship often breaks down, and the Manu'a Islands have previously gone for weeks without it calling in. This is no fun for travellers, and even worse for locals: they depend on it for food and supplies.