You're not missing anything in particular, as per other answers you can bend leads and use short lengths of wire to connect components which I often do. While it's lost poularity due to SMT technology another technique I often use is wire wrap. From that Wikipedia article here's an image of a typical connection using a traditional wire wrap post that has a square outline:
While the round shape of most through-hole component leads won't secure the wrap well I normally secure the component by soldering to the pad first, trim the lead a little and then wrap followed by a dollop of solder to secure the wire. One nice thing is that the wires are insulated so it's easy to make point-to-point connections without worrying about shorting.
While somewhat obsolete having wire wrap wire on hand is always useful even with professional work because with its very small diameter it's an excellent way to connect directly to fine pitch SMT pins to correct routing problems during prototyping.