The fastest way to find a character depends on what you already know. If you can paste the glyph, the character inspector will name it for you and break it into its constituent codepoints. If you only have a numeric reference — U+2603, 9731, or 0x2603 — the codepoint converter resolves it into every common encoding.
If you are exploring rather than searching, start with one of the lists below. The popular grid is a good warm-up. The category index groups characters by what they are — letters, marks, numbers, punctuation, symbols. The block index groups them by where they live in the codepoint space, which often corresponds to a writing system or a thematic collection like Currency Symbols or Arrows. The how-to-find-a-character guide walks through every route end-to-end.