I think the term for what you are describing is Samatha. On the Wikipedia page, you can find the "Nine mental abidings", a description of the process. There are also Zen teachings such as "The Ten Oxherding Pictures" that describe the process. Most of these teachings follow the idea of meditating "with support", using a focus (such as the mental image of a Buddha). There is also a practice of meditating "without support", as in the Essence Mahamudra of the Kagyu School.
I was also interested to see this in the above Samatha page: "
... samatha is not a strictly Buddhist meditation. Samatha in its single-pointed focus and concentration of mind is cognate with the sixth "limb" of aṣṭanga yoga', rāja yoga which is concentration (dhāraṇā). For further discussion, see the Yoga Sūtras of Patañjali."
Just a note: Advaita (Hinduism) Meditation practice is very similar to the Buddhist Mahamudra practice. Since this is a Buddhist Q&A site and the question does not seek similar practices in other religions, I won't post Advaita links here. When one gets "stuck" in one's practice, I think it is sometimes a good idea to see how other practices approach similar problems.