Once you have created and assigned a Certificate of Sponsorship to an employee, they must use the certificate to apply for a visa. This application will usually have to be made before they can start working for you.
If the individual is abroad, then they will need to apply at their local UK Visa Application Centre in the country that they are in. Processing times for visas from overseas vary, but UKVI estimate that most applications will be processed within 3 weeks of them receiving all the documents for the visa.
Most UK Visa Application Centres also offer priority services to expedite overseas applications subject to a fee. The individual should check the specific local UK Visa Application Centre they will use to determine the services offered, and the local charges for that.
If they are already lawfully inside the UK (for instance on a student visa), then they can usually apply to the Home Office in the UK (but they should check whether the rules permit switching into a different visa category before applying). Applications from inside the UK generally take longer than those made outside of the UK, but it is usually possible to pay an additional fee to have your visa application expedited.
In some cases, an individual's visa does not allow them to switch/change visa categories within the UK and those who fall into this category will usually have to leave the UK to make this application from abroad. This may also mean that any period spent in the UK prior to making their new application from overseas will not be counted for their 'continuous residence' for Indefinite Leave to Remain.
The individual will need to demonstrate that they have a valid Certificate of Sponsorship (by providing the Certificate number in their visa application) and that they meet the additional requirements in order to qualify for the visa.