Every user can rearrange their own pages. Nothing you do affects anyone else, and it can all be undone.
Gear icon (top right) → Personalise. A banner appears; now click any field, column or FactBox: move it by dragging, hide it, or set it to "show under Show more". Use + Field to add a field from the table that is not on the page (most of what people ask developers for is already in the table). On lists, drag columns to reorder and freeze a column so it stays while you scroll. Click Done.
Everything is per user and survives updates. To undo, Personalise → Clear personalisation. If a change should apply to everyone in a role, the administrator does it once at profile level (Profiles → Customise pages) instead of each person doing it. Personalise is for you; it is not a substitute for a page extension when the business depends on the change (see Designer).