How do you convert true airspeed to indicated airspeed?
Short Answer

Getting to grips with Aircraft Performance and Calibrated Airspeed are two good places to start!

The short answer:

From TAS to IAS $IAS=f(TAS)$:

$$IAS = a_0 \sqrt{5\left[\left(\frac{\frac{1}{2} \rho {TAS}^2}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} + K_i $$

From IAS to TAS $TAS=f(IAS)$:

$$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left(   \frac{ (\frac{IAS - K_i}{a_0})^2 + 1}{5}  \right)^{\frac{7}{2}} + 1 \right]} $$

WARNING: the units should be taken as SI, ($\frac{m}{s},\frac{kg}{m^3},Pa$).

In particular:


$a_0$: speed of soundat sea level in ISA condition = $290. 07 \; \frac{m}{s}$
$P_0$: static pressure at sea level in ISA condition = $1013.25 \; Pa$
$\rho$: density of the air in which you are flying $\frac{kg}{m^3}$
$IAS$: indicated Air Speed $\frac{m}{s}$
$K_i$: is a correction factor typical of your aircraft. You should find it in the POH.


How to get to this formula, see the long answer below.



Long Answer

From the definition of dynamic pressure:

$$ q_c  = \frac{1}{2} \rho v^2 $$

Where $v = TAS$, I am assuming you are interesting in subsonic speeds (cross-country flight), so we don't consider compressibility effects for the CAS:

$$CAS = a_0 \sqrt{5\left[\left(\frac{q_c}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} $$

Substituting the dynamic pressure definition in the $CAS$ as a function of $TAS$

$$CAS = a_0 \sqrt{5\left[\left(\frac{\frac{1}{2} \rho {TAS}^2}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} $$

Where $a_0$ is $295.070 \; \frac{m}{s}$ and  $P_0$ is $101325 \; Pa$. the density $\rho $ is the density at your altitude that day, you can get it from International Standard Atmosphere calculator or table/formulas.
If you measure it from your aircraft instruments $\rho = \frac{P}{RT}$, with $R=287.058 J kg ^{-1} K^{-1}$. You should give in Pressure in Pascal (not $hPa$) and most important temperature in Kelvin $K$.
Reverting the formula above (double proof is appreciated):

$$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left(   \frac{ (\frac{CAS}{a_0})^2 + 1}{5}  \right)^{\frac{7}{2}} + 1 \right]} $$

Being 
$$
IAS = CAS  + K_i \\
CAS = IAS - K_i
$$

Where $K_i$ is a correction factor typical of your aircraft. You should find it in the POH.

Finally we get TAS as a function of IAS $TAS=f(IAS)$

So:
$$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left(   \frac{ (\frac{IAS - K_i}{a_0})^2 + 1}{5}  \right)^{\frac{7}{2}} + 1 \right]} $$