The other day, when I went to attend an event, a friend of mine whom I know well came up running towards me as soon as I entered the building in which the event was held.
ご質問ありがとうございます。
"The other day,"=「先日、」
"when I went to attend an event,"=「イベントに参加しに行ったとき、」
"a friend of mine whom I know well"=「よく知っている友人が」
"came up running towards me as soon as I entered the building in which the event was held."=「私がイベントが行われている建物に入ってすぐ、私のほうに走り近づいてきた。」
ご参考までに。