What equation of state is needed for liquid states?

Supercritical fluids are well described by real and ideal gas laws.

A common equation of state for both liquids and solids is

$$V_m = C_1 + C_2 T + C_3 T^2 - C_4 p - C_5 p T$$

where $V_m$ is molar volume, $T$ is temperature, $p$ is pressure, and $C_1$, $C_2$, $C_3$, $C_4$, and $C_5$ are empirical constants, all positive and specific to each substance.

The Peng & Robinson equation of state has been found to be useful for both liquids and real gasses:

$$p = \frac{RT}{V_m - b} - \frac{a(T)}{V_m (V_m + b) + b (V_m - b)}$$

where $a$ and $b$ are empirical constants and $R$ the ideal gas constant.

For all intents and purposes, you can use an incompressible equation of state:

$$ V = constant $$

That's it. No matter what pressure and temperature, you have the same volume. It's not completely true, but in relation to gasses it is true enough to make it that pressure work is negligible in liquids compared to gasses, and for liquids, you can just deal with the heat content without considering any work done in the expansions and contractions required to change temperature.

Accurate equations of states (EOS) for real gases, liquids, or solids are (in contrast to nice theoretical models such as an ideal gas or debye solid) quite complex, and must be fitted to experimental data.

For example, a very accurate equation of state for water and steam can be found in
Wagner and Pruss, The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use, 1995
http://www.teos-10.org/pubs/Wagner_and_Pruss_2002.pdf

But the water EOS is not very intelligible, except for a computer.