Finite blocklength considerations in wireless multi-access communications are motivated by different scenarios, in particular machine-to-machine communications. It turns out that i.i.d. Gaussian inputs are not optimal for Gaussian channels with finite blocklength, and that non-i.i.d. inputs perform better but require more involved analysis. Building upon a central limit theorem (CLT) for functions, in which a sum of dependent information random variables can be viewed as a sum of functions of independent variables, we obtain a convenient approach for establishing second-order approximations of the channel coding rate for several different problems, such as the Gaussian channel with slow and fast fading as well as the Gaussian multiple access channel with a large number of users.