Obviously to start with you need to use the right kind of brush for the right paint and also what you hope to achieve on paper, wood, board or canvas.
To clean brushes where you’ve been using oils you can use turpentine or white spirits, but I feel that apart from being very stinky and so therefore not great for you to breath in, it is a little harsh on brushes. There are many brush cleaning products on the market now, even ones that are citrus based, like ‘Zest-It’, which is made from orange oil - it also smells very pleasant. I then use a brush cleaner, designed for water-colour, oils and acrylics. This ensures there is no residue left - they come in small plastic tubs with screw tops and look a bit like old-fashioned tooth powder containers (I’m going back about a hundred years now!). It looks like a hard soup inside and froths up like soap too! Finally and you may not want to do this, dry off the excess water, place the brush in your mouth, purse you lips and pull the brush out so it has a perfect point and dries with that point. You’re all going “eugh” right now, but it works and helps finer brushes retain their points. Obviously store upright, but you don’t need to be told that I’m sure!
When cleaning brushes that have been used with acrylic based paint, excess paint should be wiped off with a soft cloth or tissue and then rinsed in lukewarm water. Always make sure the water is lukewarm because hot water can damage brush hairs and cause them to fall out and in order to protect the brush further it is important to wash it with mild soap or the brush cleaner mentioned above (the toothpowder one).
This should be repeated until no paint colour comes from the brush and it returns to its original colour and shape but if it appears misshapen then use your fingers to carefully push the hairs back into place - or use my mouth-to-mouth resuscitation technique!
Good luck all and I hope everyone has a wonderful weekend!