Recently, Deep Learning (DL) models have shown promising accuracy in analysis of medical images. Alzeheimer Disease (AD), a prevalent form of dementia, uses Magnetic Resonance Imaging (MRI) scans, which is then analysed via DL models. To address the model computational constraints, Cloud Computing (CC) is integrated to operate with the DL models. Recent articles on DL-based MRI have not discussed datasets specific to different diseases, which makes it difficult to build the specific DL model. Thus, the article systematically explores a tutorial approach, where we first discuss a classification taxonomy of medical imaging datasets. Next, we present a case-study on AD MRI classification using the DL methods. We analyse three distinct models-Convolutional Neural Networks (CNN), Visual Geometry Group 16 (VGG-16), and an ensemble approach-for classification and predictive outcomes. In addition, we designed a novel framework that offers insight into how various layers interact with the dataset. Our architecture comprises an input layer, a cloud-based layer responsible for preprocessing and model execution, and a diagnostic layer that issues alerts after successful classification and prediction. According to our simulations, CNN outperformed other models with a test accuracy of 99.285%, followed by VGG-16 with 85.113%, while the ensemble model lagged with a disappointing test accuracy of 79.192%. Our cloud Computing framework serves as an efficient mechanism for medical image processing while safeguarding patient confidentiality and data privacy.