For improving monitoring and forecasting the key parameters in Geospace environment, we improved sequentially the basic elements, incorporated in the prediction procedure: a solar wind coupling function (which is a combination of solar wind parameters showing the best fit with geomagnetic activity), an appropriate geomagnetic activity index (indices), and prediction/monitoring method. (1) Going from both theoretical consideration and statistical analysis, we derived a new solar wind coupling function, which shows a better correlation with many events in the Geospace environment. Additionally to the well-known Akasofu coupling function, the new coupling function takes into account a variation of both the magnitude of cross-polar-cap electric field and the size of a region of reconnected magnetic flux in the polar caps. This coupling function takes also into account the effect of solar wind density/pressure. This leads to a significant improving the correlation between solar wind data and variations of key parameters in the Geospace environment. (2) An appropriate geomagnetic activity index should provide (a) a reasonable measure of geomagnetic activity and (b) be available in a near-real time. We developed a new, Polar Magnetic (PM) index that measure a summary geomagnetic activity from both overhead ionospheric currents and field-aligned currents flowing at the polar cap boundary. This index is computed from two geomagnetic stations located near the geomagnetic poles. Two PM indices computed for two hemispheres show high correlation between themselves and with many important parameters, and may be successfully used for real-time monitoring these parameters. (3) Using the new coupling function and new geomagnetic activity indices, we have developed an effective method for near-real-time monitoring the key ionospheric parameters such as the cross-polar-cap potential drop and Joule heating in two hemispheres, which show the energy flux coming from the solar wind into the ionosphere and energy release in high-latitude ionosphere that affects the expansion of the neutral atmosphere during and after geomagnetic disturbances which may significantly affect the satellite orbits. (4) The obtained results improve significantly monitoring and forecasting the key parameters in the Geospace environment, including the level of geomagnetic activity in two hemispheres, cross-polar-cap potential drop and Joule heating in two hemispheres, fluxes of energetic particles, and many others.