How does valerian make you calmer?
Short answer
Valerian preparations contain many compounds, but it is not known which may be responsible for its sedative effects. It is likely that there is no single active compound and that valerian's effects result from multiple constituents acting independently or synergistically (source: NIH). Overall, I think it is safe to say that valerian's sedative properties are related to its GABAergic properties (Yuan, 2004).

Background
The constituents of the volatile oil obtained from the rhizomes (underground stems), and stolons (horizontal stems) of Valeriana spec are variable due to  the variability in genetic make-up and environmental factors impinging on the batch of plants used (source: NIH). 

The major constituents include the monoterpene bornyl acetate and a variety of sesquiterpenes including valerenic acid. 

Some of the sesquiterpenes have been shown to have a direct action on the amygdala, which is a brain structure in the limbic system. The amygdala is responsible for feelings of fear and anxiety. Valerenic acid has been shown to inhibit the breakdown of GABA in the brain, resulting in sedation. GABA is the principal inhibitory neurotransmitter in the nervous system. 

The non-volatile monoterpenes known as valepotriates possess sedative activity, but their mode of action is not clearly known. The valepotriates themselves act as prodrugs, and are transformed into homobaldrinal which has sedative properties.

Extracts of valerian roots contain substantial amounts of GABA which could directly cause sedation. However, whether GABA reaches the central nervous system is debated. 

Another compound present in extracts is a lignan, hydroxypinoresinol, and it binds to benzodiazepine receptors, which are GABAA receptors and the target of benzodiazepines, i.e. tranquilizers and sedatives (Houghton, 1999).

References
- Houghton, J Pharm Pharmacol (1999); 51: 505-12
- Yuan et al., Anesth Analg (2004); 98(2): 353-8