For the majority of Springer journals, publishing an article is free of charge.
If a journal requires page charges, you will find them on the journal's springer.com homepage or in its Instructions for Authors.
Charges might apply e.g. for color figures or over-length articles. The information on these extra costs will also be available from the journal's homepage or its Instructions for Authors.
Charges for open access articles: If you choose to publish an open access article ("Springer Open Choice" article or in a "SpringerOpen" journal), there will be an Article Processing Charge (APC) to be paid by the author (or his/her funding institution). As a consequence, the article can be freely read, downloaded or distributed from SpringerOpen.com and SpringerLink by any internet user.
For the majority of BioMed Central journals, publishing an Open Access article requires a payment of the article-processing charges (APCs). More information can be found here: https://www.biomedcentral.com/getpublished/article-processing-charges