Condensation is due to excessive moisture, cold conditions, cold surfaces or inadequate ventilation. It can cause mould, heat loss and building damage. To address these issues, the room should be properly insulated and adequately heated (to keep the surfaces warm).
Condensation may still occur on replacement windows, as they'll still be the coolest surface. New windows will be more airtight than old ones, so warm moist air will be no longer be escaping through cracks in the frame and around the seals. This means that existing damp issues may become more pronounced. Many windows will include trickle vents in the frame, to allow a small amount of ventilation, but to keep the house warm and dry you may need to take a few other measures to avoid producing lots of moist air.
Drying clothes indoors can easily cause problems of damp and condensation, leading perhaps to mould, etc. So if you need to dry indoors, it should be in a room that can be shut off and ventilated (perhaps with heat recovery, as mentioned below).
The bathroom and kitchen in particular should be able to be ventilated in a controllable way, to stop moist air circulating into the rest of the house. For example, after a shower or bath, leave the bathroom door shut and the window open for a while until moist air & condensation on the window/mirror has cleared. Do the same when cooking if you can; if your home has an open plan layout at least stop the moist air circulation where possible (e.g. to the upstairs rooms).
To avoid heat loss from a room like a kitchen or bathroom, where lots of moist air is regularly produced, you could consider a heat recovery extractor fan. It may be worth getting a slightly bigger heat-recovery fan unit than you need, as they can be a bit noisy if they are operating on full power. This may be fine if are just switching it on for a short while to clear the bathroom, but it could be obtrusive in the kitchen. If a fan unit is not supplied with more solid covers over the plastic slatting, it could be worth fitting something if you live in a house that is a bit exposed to the wind (as they could let in draughts when not in use). An openable wooden casing could be fitted quite easily.
If drying clothes indoors is not an issue, and you're already careful about venting away moisture from bathroom & kitchen, then excessive condensation may be from some other cause, such as a water leak somewhere (e.g. from a pipe under the floor or in the loft), or water penetrating the structure from outside (such as rainwater coming in cracks in masonry, or if gutters are broken). If problems persist, it would be worth investigating these issues, as over time they'll cause damage to the building.