Email hosting company is usually defined by MX records that point incoming emails to a particular provider — who then processes those messages. In order to find the MX records, it’s necessary to perform an MX lookup. For example, if your email address is yourname@yourdomain.com you need to look up MX records for yourdomain.com.
Free online services such as MXtoolbox will give you a list of MX records that usually offer a provider’s name and corresponding IP addresses records. Sometimes, though, a domain can have a custom domain-based email MX record (e.g. mail.yourdomain.com). If that’s the case, you should also perform a Whois search on one of the IP addresses. That will give you the name of the email provider. Using free online services such as Network Tools is great for this.