Stripping and varnishing stairs is a big and messy job, requiring lots of preparation, physical effort and time. It could take you a week or more to complete the project properly, if working alone. Further, the stairs will be inaccessible for several hours at a time while the varnish dries. However, the end result is likely to be well worth all the effort.
Follow the advice of Jim Sulski from House Task and use a heat gun to strip the existing paint or varnish finish from the stairs. Heat guns are usually referred to as hot air guns in the UK. Plug the hot air gun into an extension cable to give you more reach.
Point the nozzle of the hot air gun at the existing surface, keeping it about 10 cm away to avoid scorching. When the existing surface starts to melt and bubble, scrape it off with a scraper. Some varnishes are very sticky and will tend to adhere to your scraper. You may need a second scraper to scrape away clumps of stuck varnish from your first scraper.
Continue the process of applying heat and scraping until you have removed the entire existing surface. Use the nose of a triangular scraper to get into small areas, such as decorative detailing on spindles. Alternatively, use paint and varnish stripper to strip the existing finish.
Sand the stairs when you have removed the existing finish. The surfaces are likely to be rough because of small remaining amounts of congealed paint or varnish. Work in the direction of the grain to prevent cross-grain scratches. Use an electric sander with care as it is easy to inadvertently remove too much material.
Sand by hand in areas that are difficult to access. This includes around spindles, which are usually slender. Follow the advice of Remmers and use 100 to 120 grit sandpaper.
Wrap the sandpaper around a sanding block to make it easier to use. Move the block backwards and forwards over the rough surfaces until they are smooth. Vacuum the stairs after sanding to remove all traces of dust.
Plan to start varnishing at the top of the stairs and work downwards. This is so you will not be stuck upstairs after completing the job. Open the varnish and stir it well, unless otherwise indicated on the can.
Dip your brush into the varnish and take up an amount that does not drip. Wipe off your brush as necessary on the side of the can. Apply varnish to every surface. This includes tread, riser, newel and cap, spindles and handrail.
Set up a step ladder at the side of the staircase, if necessary, to access any areas you cannot easily reach while standing on the staircase. Follow advice on the can to leave enough time for the varnish to dry. Apply a further one or two coats, sanding down lightly between coats if the surface is rough.
Wear a dust mask, goggles and protective gloves. Use chemicals carefully, following product safety advice.