WSLには開発用ツールが入っていませんので、まずはbuild-essentialをインストールします(あとでもいいかも?)。
sudo apt install build-essential
Homebrewの公式HPにも記載のある次のコマンドを実行します。
sh -c "$(curl -fsSL https://raw.githubusercontent.com/Linuxbrew/install/master/install.sh)"
次の変数を~/.profileに追加します。
export HOMEBREW_PREFIX="/home/linuxbrew/.linuxbrew"
export HOMEBREW_CELLAR="/home/linuxbrew/.linuxbrew/Cellar"
export HOMEBREW_REPOSITORY="/home/linuxbrew/.linuxbrew/Homebrew"
export PATH="/home/linuxbrew/.linuxbrew/bin:/home/linuxbrew/.linuxbrew/sbin:$PATH"
export MANPATH="/home/linuxbrew/.linuxbrew/share/man:$MANPATH"
export INFOPATH="/home/linuxbrew/.linuxbrew/share/info:$INFOPATH"