Without using sharing rules how can i share records to another user?
For automated sharing, where possible it is far easier to use Sharing Rules than other forms of sharing. If you really cannot use Sharing Rules, there are options such as Apex Sharing, though these require explicit coding to support them and, if you want to make it possible to support this approach regardless of the Org Wide Defaults for sharing, you have to be careful to use entirely dynamic DML when creating or deleting the sharing records since the sharing record objects only "appear" in your org when OWDs are not Public Read/Write.
Of course, if you are not automating this, your users can now use manual sharing even in Lightning Experience.
See the documentation for more details on the various forms of sharing.