To answer this question, we need to take in account the several factors that will decide how and how much they are paid:
- The number of pages drawn for each issues (20 pages or more).
- The regularity of his work (weekly, monthly...).
- The experience of the mangaka (newcomer, experienced...).
- The popularity of the mangaka's work (that 2002 manga you have never heard of, One Piece...).
- The publishing company (Akita Shoten, Shueisha...).
- The merchandising around his work and the anime adaptations.
Number of pages drawn and regularity of the work
A mangaka is paid depending on the number of pages he is drawing. The most typical case for mangakas are the newcomers who are publishing a standard chapter of 16-20 pages every week, so we are gonna base our numbers on this common case. Usually, a publisher will pay between 10,000¥ and 12,000¥ per page created to a starting artist. Considering he would draw 80 pages per month, it would lead to a monthly outcome going from 800,000¥ to 960,000¥.
Be careful: this is what a starting mangaka usually win per month. But this is not what he is really getting in the end. A mangaka usually needs to pay his own material, his assistants, his studio if he has one, and other different kind of expenses.
It is also important to mention that colored pages are paid more than normal pages (~ 1.5x more).
Now, I have talked about the typical weekly case. In this particular case, a mangaka usually draw between 16 and 20 pages per chapter (for instance One Piece). But another really common case are the monthly releases (for instance Ao no Exorcist). The number of pages will vary a lot, but you can consider there is usually between 35 and 50 pages drawn per month in such cases. And the price per pages is not necessarily higher, as it is most of the time the same.
The experience of the mangaka
The previous numbers are mostly applying to starting mangakas. But those who have already worked for a long time in the manga industry can obtain an increased outcome per page drawn. One mangaka, Sato Shuuhou, published in 2009 the average payment he was getting by page drawn through the years. While he was getting 10,000¥ per page in 1998 for the Umizaru manga, he was getting 25,000¥ per page in 2006 for the Tokko no Shima manga, and 35,000¥ in 2009 for the Say Hello to Black Jack manga. Of course, those numbers are not representative of every mangaka and should not be taken as a constant.
The popularity of the mangaka's work
Another important factor is the popularity of the chapters and of the final mangas. A famous exemple is the Weekly Shonen Jump popularity vote. Each reader has the possibility every week to fill a paper on which he is ranking his 3 favorite chapters of the week, and send it back to Shueisha (the Weekly Shonen Jump publisher). The total number of votes are then calculated, and the publisher get an intern result for the popularity of the published mangas. If a published manga is staying way too long in the lower ranks, it might stopped to be published (at least on this magazine). The other way, if a manga is often staying in the best ranks, it means that it is interesting a lot of readers, readers that might buy another issue of the magazine because of this particular manga. Because of this, the publisher may increase the outcome won per page by the mangaka. It is also depending on some other factors, like if there is an anime adaptation or some good manga sales, but it will be explained on the next point.
The publishing company
Depending if the publisher is a totally unknown one or the really famous Shueisha, it might happen that the number of outcome given per page is lower or higher. This is of course depending on the politic and the financial resources of the publishing company.
The merchandising around his work and the anime adaptations
Obviously, there might be some merchandising around the work of a mangaka, and of course some anime adaptations for one or several mangas. For this particular part, I will let you check this question which is describing it pretty well.