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.
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.