How to check what is the percentage of charge in my lead acid battery?
That looks like a lead acid battery with 2 cells. Luckily, assuming a relatively healthy battery you can get a rough idea of the charge level by just measuring the open circuit voltage.

Here's a table of values for some rough voltages to expect (computed using value from here)

100%: 4.22V
75%:  4.15V
50%:  4.08V
25%:  4.02V
0%:   3.96V


If you want to go more in depth, I would recommend reading this page, as well as the links inside that page. The short answer is "it's complicated", and specialized equipment is probably the best answer.