It is estimated that between 50% and 75% of all cases of dementia are due to Alzheimer's disease (AD), the most common neurodegenerative disease among World population. However, a long preclinical period of AD makes it difficult to differentiate between people with Mild Cognitive Impairment (MCI) that would progress to dementia from people with MCI that would not. One of the most promising solutions to detect MCI which will evolve to dementia (preAD) comes from the field of automatic speech analysis. Speech is a complex physiological and neurocognitive language-mediated process, which can be significantly altered in pathological aging and exhibit high levels of sensitivity for the diagnosis of neurological diseases. The purpose of this research is to offer a detailed perspective on the speech changes in MCI and mild AD when compared to healthy aging (HA), that would allow to detect pathological processes prior to the clinical expression of AD. Based on our previous research record on speech in HA, MCI and AD, we provide a global review of dementia-related speech traits and propose a reading-based protocol for assessing ongoing neurodegenerative processes in the elderly. We report the results of speech analysis in elderly people with different cognitive profiles, who performed a standardized reading task and were further analyzed for correlations between neurocognitive assessment indicative of cognitive impairment stage (HA, MCI or AD) and acoustic, temporal and prosodic traits in speech. We show that evolution from HA to AD exhibits a steady pattern of speech changes in parallel to the cognitive decline, which consists in significant increase in duration and phonation time, extension of pauses and voice breaks, intensification of variation in syllabic production, and decrease in speech energy and intensity leading to dysphony. In doing so, we prove that a standardized reading task is a very useful type of stimuli for detecting dementia-related speech traits and, in view of this, we discuss the relevance of reading for preclinical automated diagnosis of AD. The main contribution of this paper is a corpus of recordings of the standardized reading task performed by healthy elderly people and people with MCI and AD in Spanish language, and which can be used for further research purposes. In this respect, our work fills an important gap existing in corpora-based studies of speech and language impairments related to progression to dementia.