I want to use magento rest api authorization for my web application customers, I found in docs that there is /customers/:customerId request, to get information about user, but I can't understand, how to get customerId to make this request. Is there such a method in Magento REST API and if not, how I can get authorized customer Id via REST API.
There is a REST service to get a list of all existing customers and their customerId. Its a GET request to /customers. You can find its description in the REST API docs http://www.magentocommerce.com/api/rest/Resources/resource_customers.html#RESTAPI-Resource-Customers-HTTPMethod-GET-customers
Unfortunately there is no service to authenticate users using username and password that I know of. Not even in the SOAP API that has much more services than the REST API.