If you find it difficult to see how judo could work as self-defence, here's an entertaining 2 minute clip from the 1945 movie Blood in the Sun with actor (and Judo black-belt) James Cagney:
The core techniques of Classical Judo include:
- The art of falling: Breakfalls and rolls
- Methods of disturbing the opponent's balance
- Throwing techniques
- 15 leg throws
- 15 hip throws
- 6 shoulder throws
- 10 hand throws
- 15 "sacrifice" throws
Many of these techniques are clearly unsuitable for sport competition -- neck dislocations, anyone? -- and have accordingly been dropped from Olympic Judo because they do not serve its aims. But for effective self-defense, and as part of a rich cultural inheritance, they retain their place within Classical Judo.
One of the characteristics of Judo is taking a grip of your partner's jacket, but as they say in the Chinese martial arts, "Masters refrain from people that simply grab a hold of you like they are falling off a 100 story high rise, and won't let go". The taking of a grip is a convenience of practice, and a convention in Judo competition, but with appropriate training and sufficient experience, it becomes feasible to flow between striking and grappling, and to throw an opponent without necessarily grabbing.
With a foundation in Classical Judo, it is not so hard to supplement this basis with additional techniques of Jiu-Jitsu, including striking (including vital points), restraint & control (arresting techniques, typically joint-locks), and tactics for common self-defense scenarios.
Lastly, it is worth describing the meaning of "judo" and "jiu-jitsu". Usually, these are translated as "ju" (or "jiu") = gentle, "do" = way, "jitsu" = art. So "judo" = gentle way, and "jiu-jitsu" = gentle art. But another translation of "ju" is flexible or adaptable, making Classical Judo the flexible way, adaptable to any situation.