1. Now I get exercise by taking him for a walkevery day.
现在我每天借着遛狗运动一下。
by doing sth.表示“通过某种方式”，用how引导的特殊疑问句提问。
--How do you learn English?
--I learn Englislh by listening to cassettes.

2. ...and she also takes part in the training with us.她和我们参加同样的训练。
take part in指参加活动，如体育运动、比赛、游戏或讨论,含有积极参与并发挥作用之意,多用于正式场合。
l take part in all kinds of after-school activity.Would you like to take part in the party?

注意与join和join in的区别:
join多指加入某一个组织或某些人，成为其中一员。join in 指参加活动，在口语中可与take part in通用。We both joined the Labor Party.
我们俩都加入了工党。
They all join in singing the song.他们一起唱这首歌。