All the examples on DNA cloning I have encountered have assumed that the target gene and vector both have compatible restriction sites at just the right locations (probably for ease of explanation). Instead suppose I have a vector that has restriction sites for multiple restriction enzymes, but my target DNA sequence doesn’t have a restriction site for any of them, how would I go about creating a recombinant DNA from these?
If you're synthesizing the insert then you just design it with restriction sites that are compatible to the vector. Otherwise, you can design PCR primers that have restriction sites in them. That way when you amplify your insert you'll attach the restriction sites to it. EMBL, Addgene, and NEB all offer somewhat more detailed explanations of this on their sites.