Large Language Models (LLMs) like ChatGPT, Llama, or Mistral generate text by predicting the next token based on previous ones using a vector of logits, which are transformed into token probabilities via the softmax function. Post-processing techniques such as greedy decoding, beam search, and sampling strategies (top-k and top-p) are utilized to refine the selection of these tokens, balancing between predictability and creativity. Advanced methods, including frequency penalties, logit bias, and structured outputs achieved through prompt engineering or fine-tuning, offer further control over the generated text. Parameters such as "temperature" influence this process by adjusting the diversity and predictability of outputs. These techniques enhance the utility of LLMs across various applications, from generating creative narratives to producing structured data formats like JSON and SQL. The article also highlights the challenges in implementing these methods and recommends tools such as OpenAI's API and libraries like Hugging Face's transformer for efficient text generation and output customization.