Buses used to be the main means of transportation for the Chinese people.
Used to be...【曾是......】；main=major=chief【主要的】；the means of transportation【交通工具】
In recent years，with the number of private cars increasing，cities have been facing increasingly severe traffic problems.
with随着；the number of...【......的数量】；increasing增多；In recent years近年来（现在完成进行时）；face increasingly severe+名词【......越来越严重】
To encourage more people to travel by bus，many cities have been making efforts to improve their bus service quality.
To【为了......】；encourage sb to do sth【鼓励某人做某事】；make efforts to do sth【努力做某事】
Bus facilities have been continuously renovated，and the bus speed has also increased dramatically.
Renovate=update更新；continuously不断地/连续地； bus speed车速；dramatically显著=significantly=remarkably
However，bus fares are still quite cheap.
Bus fares公交车的价格；are still依然=remain（这两个+形容词作表语）；cheap廉价=low=affordable
Now，in most cities，many local elderly citizens can make a bus for free.
In most cities在大多数城市；make a bus for free免费乘坐公交车