1) robo410 is right - start using your hands. when you measure smaller amounts, put it in the palm of your hand and see how much it is. for larger amounts, like a cup of flour, scoop up a big handful into a measuring cup and see how much it comes to. if you're making pancakes or bread or muffins and putting the same amount of flour into the same bowl every time, try to remember how big of a mound it makes in the bowl.
2) people may scream, but let me pooh pooh those who talk about the chemistry of baking and the importance of correctly measuring. when i worked as a pastry chef, i measured every ingredient to the nearest gram. why? because in the restaurant industry product consistency is the name of the game. when i make a genoise at home, i don't bother. i use the same number of eggs and probably about the same amount of a stick of butter more or less every time. but to me, sifting in the "right" amount of flour amounts to the same as knowing how long to beat the eggs and sugar over the heat: until it looks right. how much sugar i put in depends on how sweet (and how moist) i want it to be. same if i want to substitute some cocoa powder or almond flour for some, or even all, of the flour.
3) ok. now that i've offended everyone, let me do an about face and say that all those people i just pooh poohed are actually correct.... at least to a point. baking
is all about chemistry and how things react with each other. depending on the product, there can be a lot of leeway in ratios... but only to a point. knowing your ingredients coupled with a lot of experience is all it takes to become a "natural" cook.
4) if you aspire to becoming a natural cook like your dad and being able to just "throw things together", start with something really forgiving, like soups. if you start with a decent stock and don't go overboard with the salt, it 's hard to go wrong with a soup. spaghetti sauce is another good one. how thick do you want it? how spicy? what kinds of spice? lots of leeway here too. eyeball and taste, eyeball and taste.
as far as baking goes, i'd suggest starting off with something like pancakes. start making them every sunday. little by little start eyeballing the ingredients, and ween yourself away from the measuring cups and spoons. if you can do pancakes, then you can try throwing in another handful or two of sugar and add only enough milk so you get a really soft dough that you can pat or roll out, and fry up some doughnuts. bread is also forgiving. start by following a bread or pizza dough recipe and try to get a feel for the consistency of the dough. when you have a general idea of how soft or stiff a dough you want, there's no need to measure out the flour at all. add enough flour to your liquids until it makes a stiff paste that's hard to stir with a wooden spoon. another large handful or so will make it into a ball that you can start kneading. after that, it's just dust your board with flour and knead it in until it's the consistency you want. trying softer and stiffer doughs is how you learn to achieve the results you want.
if you can work your way to being able to "throw together" these things, you'll be well on your way to becoming a "natural cook".
i'd say "go for it!"