stuff your nose with tissue until the bleeding stops. Also, applying pressure can help to stop a nosebleed.
鼻血- Nosebleed
止まるまで- Until it stops
つっぺしといて - stuff your nose with (tissue)
止血 - stop bleeding
基本 - Fundamental, standard
圧迫- Pressure
「鼻血止まるまで、つっぺしといてね。止血の基本は圧迫だよ」は英語で - (You should) stuff your nose with tissue until the bleeding stops. Also, applying (a bit of) pressure can help to stop a nosebleed.
You should - ～をした方がいい
a bit of - 少し
Can help to - 役に立つ
イギリス 
