He saw a flying bird and raised his bow.和I saw forty horses

a flying bird 这里现在分词当形容词用,一只“当时” 正在天上飞着的鸟.
running in the sports field 是宾语补语,running 是非谓语（现在分词）引导后面的从句用来修饰宾语 horses.
go 这个词后面常加动词,你想必清楚.比如 go shopping；go fishing 等等.
这句 how about 后面必须跟名词性质的单词、词组,因此必须是动名词 going 的形式+要去做的事 fishing