Erbium-doped thin-film lithium niobate (Er:TFLN) provides efficient solutions for monolithic integrated waveguide amplifiers and lasers, as well as the potential for electro-optic modulation and nonlinear application. However, the gain and saturation absorption characteristics usually lack dynamic analysis, which is highly valuable for various gain devices. We provide a practical framework for correlating the erbium absorption and signal wavelength/power in the erbium-doped waveguide amplifier (EDWA) on the Er:TFLN platform, demonstrating the gain performance of single-wavelength or multiwavelength signal amplification. The 10 cm long Er:TFLN EDWA achieves 62.76 dB signal enhancement at 1531 nm, with 22.26 dB internal net gain at the small signal region. Additionally, a significant on-chip output power of 16.65 dBm with 7.65 dB internal net gain is realized at 1550 nm. Furthermore, theoretical models and experimental results have been conducted on signal saturation power, output power, and noise figure. In multiwavelength signal amplification experiments, approximately 20 dB internal net gain and a noise figure of 4.36 dB are achieved for an electro-optic frequency comb with a 10 GHz repetition rate. Moreover, an internal net gain exceeding 20 dB is achieved across 45% of C-band broadband signals, establishing a solid foundation for relay amplification applications in highcapacity and multichannel data transmission systems. The gain dynamics proposed in this work can be effectively applied to design optimal EDWAs and lasers to construct monolithic integrated lithium niobate systems.