APEX: Access Sharing Programatically

For Standard Objects:
AcountShare
ContactShare
OpportunityShare
.......

For Custom Objects:
MyCustomObject__Share

Properties:
AccessLevel
ParentID
RowCause
UserOrGroupdId

Examples:
MyCustomObject__Share myObj = new MyCustomObject__Share();

myObj.AccessLevel = 'Read';

myObj.ParentID = someId;

myObj.RowCause = Schema.MyCustomObject__Share.Manual;

myObj.UserOrGroupId = someUserOrGroupId;

For more information: https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_bulk_sharing_creating_with_apex.htm