I’d second the “talk to yourself” approach. I’ve never used the service, but others have also recommended italki (note that it’s a paid service, however).
Like anything, speaking is almost entirely just a matter of practice. The more you do it, the easier it gets.
There are several aspects to speaking:
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Production vs. recall. Wanikani focuses on recall and recognition, not production. It shows you characters and quizzes you on the meaning and reading. Production is the other way around: you want to go from a meaning (what you want to say) to the reading. It’s the same as writing vs. reading: more reading and immersion definitely helps, but if you want to get good at writing you’ll need to actually write.
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Shyness and fear of mistakes. This also succumbs to practice and repetition. Once you make a few mistakes in a conversation and realize the world didn’t end it gets easier.
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Pronunciation. Learning to hear the differences in Japanese pronunciation is the first step to being able to reproduce them on your own. Can you hear the difference between おばさん and おばあさん? Between きて and きって? Unsurprisingly, this also succumbs to practice and repetition.
Some specific advice:
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I’ve started practicing production using the self-study quiz for new items in my review queue (stuff in SRS stages 1-2). It can be configured to display the meaning of an item and quiz you on how you would say it in Japanese (you reply with the hiragana). Limiting yourself to just items in SRS stages 1 and 2 lets you practice without getting too bogged down with synonyms and homonyms (you’ll know which specific term they are after because you’ve seen it recently). There are also things like kamesame and kaniwani focused specifically on production.
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Enable “autoplay audio in lessons/reviews” in your settings (wear headphones if you’re worried about annoying others nearby). The more you can immerse yourself in proper pronunciation, the more you’ll be able to speak things correctly. Try to imitate the sounds as you hear them (subvocalizing is fine, you don’t really need to say them aloud but that’s even better if you’re alone).
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Really focus on “hearing” the words as you respond during the reviews (before the audio autoplays). Imagine yourself saying the word aloud (or, better, actually say it aloud if you can).
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If you’re fortunate enough to live someplace with a reasonably large Japanese community, look for someplace nearby where native Japanese speakers are likely to be found: Japanese grocery stores, bookstores, kendo/karate/aikido/judo dojo, Buddhist churches, etc. If they have a bulletin board, put up a notice offering English conversation practice in exchange for Japanese conversation practice.
Where there’s will, there’s a way.