Many countries require the use of a so called trunk prefix for national calls. A trunk prefix is, in most cases, a single digit code, often 0, added before the national subscriber number. This code must be left out when dialing in from abroad.
Here's a trunk prefix list for all countries using one. Note that there are 2 countries where, for some phone numbers, the initial zero is part of the actual phone number so there is no need to remove it: Italy and Ivory Coast.
Most telephone service providers (fixed and wireless) have the option to block international calling. Some even have this as a default feature while some smaller, often prepaid wireless plans may not even feature these types of calls. So, before trying to place a direct international call make sure your calling service allows it.
In most countries other than the USA and Canada cell phone numbers do not use area codes. Instead, they use a unified national dialing format, usually being allotted one or more starting digits not used by landlines/geographic area codes. On this website, for each country, we highlight the difference between landline and mobile numbers. There are a few countries such as Mexico, Brazil or Argentina which do use area codes for cell numbers - this is clearly pointed out on the pages in question.
Often people try to dial toll free numbers advertised by foreign businesses. Companies use these special types of telephone numbers to encourage their customers to call them free of charge. Note however that toll free numbers are only designed to be dialed at a national level, from within their issuing country. Companies or individuals owning a toll free number have the option to block incoming international calls and often do so. Moreover, some carriers will not even connect these types of international calls or, if they do, the caller is always charged for the call.
So, you can try dialing a foreign toll free number. If you are lucky and it works expect to pay for the call. If it doesn't work look for a regular telephone contact - serious businesses will give their international callers this option. Read more on dialing toll free numbers internationally
A feature offered by some VoIP service providers is to call internationally without dialing 011 first if you are in the US. Having this feature turned on usually means that you should leave out the 011 Exit code or your might not be able to call.