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There are statements in wiki like:

The current measurement of the age of the universe is 13.799±0.021 billion (109) years within the Lambda-CDM concordance model.

My question is how does scientists theorize this value, by relying on which observed facts and data?

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The age of the universe $t_0$ is computed in any cosmological model according to,

$$H_0t_0 = \int_0^\infty \frac{dz}{(1+z)E(z)}$$

where,

$$E(z) = \left[\Omega_{\mathrm{matter}}(1+z)^3 + \Omega_{R}(1+z)^2 + \Omega_\Lambda\right]^{1/2}$$

where $\Omega_{\mathrm{matter}}$ is the matter fraction, $\Omega_\Lambda$ is the vacuum energy contribution and $\Omega_R$ is the curvature contribution; baryon matter is included in $\Omega_{\mathrm{matter}}$. In $\Lambda\mathrm{CDM}$, one has $\Omega_{\mathrm{matter}} = 0.26$, $\Omega_{\Lambda}= 0.74$ and $\Omega_{R} = 0$. The observed value of $H_0 = 71 \, \mathrm{km \, s^{-1} \, Mpc^{-1}}$ leads to,

$$t_0 \approx 13.7 \, \mathrm{billion \, yrs}.$$

The parameters of the model are found in the Planck mission paper. In general, for a flat model, by performing the integral one finds,

$$t_0 = \frac{1}{3H_0 \Omega^{1/2}_\Lambda} \log \left( \frac{2}{1-\Omega^{1/2}_\Lambda}-1\right).$$

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