Can a Cuban travel to Canada for vacation??

I have a friend who lives in Cuba who I would love to come visit me in Canada. I do not know how thing's work in Cuba or how strict they are. But would he be able to come to Canada for a vacation and if so how can this be done?

Yes they technically Can..They Must Go to The Canadian Embassy in Havana and apply for a visitors visa.Once this visa is issued they must apply for an Vacation Abroad permit and from there you can buy their plane ticket.
In order to apply for the Visa they need
Temporary Resident (Visitor) Visa applications should be submitted at least 21 days before the expected day of departure.
In most cases, the processing of a visa application requires between one and three weeks, sometimes more. You should submit your visitor visa application at least 21 days before your expected day of departure. If possible, submit your application 2 or 3 months before departure.

If you have travelled frequently to Canada in the past, we encourage you to apply for a multiple entry visa.
How to Apply for a Temporary Resident (Visitor) Visa.

If you are visiting friends or family (i.e. a private visit), you must submit the following with your application:
Application for a Temporary Resident Visa and Havana Supplementary form fully completed and signed.
A valid passport valid for at least 12 months.
Old passports bearing proof of previous travel abroad, if applicable.
Two recent passport-size photos of each traveller (with the traveller's full name written on the back).
Letter from employer indicating length of service, salary and period given for vacations, if applicable.
Proof of financial situation, salary receipts, deeds on properties, etc. Applicants must submit original documents and a set of copies.
If you are going to Canada to visit friends or relatives, you will need a fax or letter of invitation from Canada providing details of the purpose of the invitation. The invitation does not need to be certified at the Cuban Embassy or Consulate in Canada. The invitation must include the full name, contact details, immigration status, and signature of the person inviting you, as well as proof of his / her financial situation (Income tax notice of assessment, employment letter, bank statement, etc).
If you are under the age of 16 and travelling alone or with only one parent, you will require a notarized authorization to travel from the non-accompanying parent(s).
Photocopies of the identification cards of the immediate members of your family ( children and spouse).
Fee payment at Banco Metropolitano.
Photocopies of the birth certificates or national ID cards of you children in Cuba, whether or not they are travelling, if applicable.
:

All the information you wish to be considered when assessing your application, should be submitted in writing along with the paper application. You must choose yourself and submit in writing all the documents and reasons that you consider relevant to satisfy the visa officer that you are a bona fide temporary resident to Canada.
The visa officer will conduct a personal interview only when there is insufficient information on the paper application to make an informed decision, or when clarifications are necessary. Your application will be assessed on the basis of the documentation you submit. Failure to provide complete, truthful and accurate material may result in your application being refused, possibly without an interview.We require only one application per family unit. Dependent children 18 and older should complete and sign their own application form. Dependent children 16 and older should be available for interview.

Fee Schedule for Immigration Services
Please note that fees in Cuban Convertible Pesos (CUC) are subject to change at any time due to fluctuations in the exchange rate.

There are 3 ways to pay fees for immigration and visa services:
in Cuban Convertible Pesos (CUC) at three branches of Banco Metropolitano in Havana. The bank charges the applicant a $1.00 CUC fee for this service. Two Bank receipts must be presented at the time of your application to the Visa Office at the Canadian Embassy in Havana;
in Canadian dollars in cash at the Immigration Receptionist window. Only the exact fee is accepted as the cashier cannot give change;
in Canadian dollars by a certified cheque or money order made payable to the Receiver General for Canada drawn on a bank in Canada.
Please ensure that you obtain a receipt for fees paid.

BANK LOCATIONS:
Banco Metropolitano, Oficina Central, 5ta. Ave. y 112, Miramar, Ciudad de La Habana, Telephone: (537) 204- 3869. Open Monday-Saturday, 8:30am-3:00pm

Banco Metropolitano, Sucursal 9073, LÃ*nea y M, Vedado, Ciudad de La Habana, Telephone (537) 832-2006, (537) 55-3116, (537) 55-3117, (537) 834-4241, Open Monday-Saturday, 8:30am-3:00pm

Banco Metropolitano, Sucursal 9074, Montserrate y San Jose, Habana Vieja, Ciudad de La Habana, Telephone: (537) 863-3953. Open Monday-Saturday, 8:30am-3:00pm

Application for Temporary Residence
Single Entry
75 Canadian dollars
70 Cuban Pesos

Multiple Entry
150 Canadian Dollars
140 Cuban Pesos

Cuban citizens are NOT free to travel abroad...why do you think they risk their lives floating to florida on rickety rafts? they are virtual prisoners in their own country. the gov't may say they can travel if they meet certain requirements, but they make sure they cannot meet the requirements. or, the family of the person is jailed or worse if a person is allowed to travel and does not return...that is not exactly freedom to travel.

That kind of things vary veeeeeeeery frequently. You should check with the Cuban consulate

Technically yes, practically no.

Jc22ny have given you the right information....you can 'sponsor' their visit....there is paperwork involved, but it is possible. Many have done it and it is legally possible.
Just take a look at Jc22ny information to go about it the right way.