Traditional search systems focus on query formulation for effective results but face challenges in scenarios such as product searches where crucial product details (e.g., size, color) remain concealed until users visit specific product pages. This highlights the need for intelligent web navigation agents capable of formulating queries and navigating web pages according to users' high-level intents. In response to this need, this work introduces a Grounded Language Agent for Intelligent Web Interactions, called GLAINTEL. Drawing upon advancements in language modeling and reinforcement learning, GLAINTEL investigates the efficacy of transformer-based models in enhancing the search capabilities of interactive web environments. Given the dynamic action space for each state in web navigation, GLAINTEL employs the Flan-T5 architecture and incorporates language modeling and value estimation heads. This work focuses on training smaller language models as agents across various scenarios, systematically evaluating the impact of human demonstrations on the training process. Specifically, we investigate scenarios where no human demonstrations are available and subsequently assess the effective utilization of such demonstrations. We also explore unsupervised domain adaptation for situations where demonstrations are confined to a specific domain. Experimental evaluations across diverse setups demonstrate the effectiveness of training agents in unsupervised settings, outperforming in-context learning-based approaches that employ larger models with up to 540 billion parameters. Surprisingly, behavioral cloning-based methods that straightforwardly use human demonstrations do not outperform unsupervised learning-based methods. Additionally, combining human demonstrations with Reinforcement Learning-based training yields results comparable to models utilizing GPT-4.