1. Usage of 着(zhe):着 follows a verb mostly, .sometimes follows an adj.
eg.1 唱着歌(to be singing a song) eg.2 低着头
2. Meaning of 着(zhe):着 doesn't has a substantive meaning itself, but indicate a continuous process of an action of the verb coming before 着,or indicate a status described by the preceding adj..
3. When there are two verbs in a sentence describing a major action and its accompanying action, 着 goes after the accompanying one.
eg.1 听着歌跑步
4. Difference of With 着 and Without 着:
eg. 挂一幅画 put a painting on spl.
挂着一幅画 there is a painting hanging on spl.