When you say “speak”, it’s important to note that you will NOT be mastering the language in this time. You can absolutely speak it to certain degrees of competence, but you can’t do work in 3 or 4 months and then be done for good. Defining this degree of competence is important so that you have a realistic goal, and know what you will NOT be able to do.
What many people in experienced language learning communities do is base their goals on something called the Common European Framework of Reference for Languages. The Wikipedia link can give you a better idea of what each level involves.
Where you actually aim brings us to the next important definition:
What do you mean by 3 or 4 months?
For a lot of people, this involves a casual investment of an hour or so a week.In reality, the amount of months doesn’t matter, it’s the amount of hours.
You may learn more in a single intensive week of full-time learning than you would in 4 months of casual hour-a-week passive learning. As such, your level of dedication in the 3-4 month period dictates how far you will go.
We are all busy, but successful language learners replace “I don’t have the time” mentalities with “How can I make the time?” ones. You give up TV (in the wrong language) and other time-black-holes, you decide to invest every spare second into your project, and you even take time off work if possible.
If you can devote 4-6 hours a day, every single day for the next months, then you could reach a B1 (lower intermediate) stage in your language if it’s your first one. You could even reach upper intermediate if you have experience learning languages already, or even higher depending on if you know a similar language. How far you go is a nebulous region that depends on many factors, most of which are centered on your motivation and drive.
Learning To Speak
Ok, with that all out of the way, the actual method is outlined in your question already. You don’t want to “learn a language”, you want to LEARN TO SPEAK a language. As such, speaking must be the center of your work and goals. Many traditional courses miss this and make speaking an afterthought after reading/writing and grammar drills.
You don’t need 3 or 4 months – you can speak your language this very week (as an absolute beginner) if you put yourself in front of a native speaker and try to use whatever you can as imaginatively as you can. You take a few words and you say them immediately, and you get feedback to improve.
Generally, I recommend people use a site like Italki.com to find conversation partners (free) or private teachers (paid, but affordable if you take advantage of currency differences), and book a session every single day for the duration of the project. You will get so much practice that improving is the only option.