Let $F$ be a field whose characteristic is not $2$ and $K=F\left(t\right)$. We give a simple algorithm to find, given $a,b,c\in K^{*}$, a nontrivial solution in $K$ (if it exists) to the equation $a{X}^2+b{Y}^2+c{Z}^2=0$. The algorithm requires, in certain cases, the solution of a similar equation with coefficients in $F$; hence we obtain a recursive algorithm for solving diagonal conics over $\mathbb{Q}(t_1,\cdots ,t_n)$ (using existing algorithms for such equations over $\mathbb{Q}$) and over ${𝔽}_q(t_1,\cdots ,t_n)$.