uv is a single static binary. Two install paths.
Standalone installer (recommended): curl -LsSf https://astral.sh/uv/install.sh | sh. The installer drops the binary at ~/.local/bin/uv (or similar) and adds it to your PATH. Restart your shell.
Homebrew: brew install uv. Slower install but keeps uv in your Brewfile.
Verify with uv --version. Upgrade with uv self update (the standalone installer's upgrade) or brew upgrade uv.
uv ships fast — typically a release every 1-2 weeks. Upgrade often.