For $d=1$ non-censored and $d=0$ censored observations with the censoring point $\gamma$, Tobit regressions estimate $$$$f(y_i) = \left[ \frac{1}{\sqrt{2\pi \sigma^2}} exp \left(-\frac{1}{2\sigma^2}(y_i-x'_i\beta)^2\right) \right]^{d_i} \left[\Phi \left(\frac{\gamma - x'_i\beta}{\sigma}\right) \right]^{1-d_i}$$$$ via maximum likelihood (which requires that the errors are $\epsilon_i \sim N(0,\sigma^2)$). Under less strict assumptions it is also possible to use a two-step estimator in which the first step uses a Probit model to predict the censored outcomes (see Cameron and Trivedi (2009) for details).