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。
When I went in the building, he came running over toward me.
この場合、次のような言い方ができますよ。
ーWhen I went in the building, he came running over toward me.
「建物に入ると彼が走って近づいてきた」
to come running over toward me で「私の方に走ってやってくる」
ご参考まで！
アメリカ合衆国 
カナダ 
