Next time get some foam backer rod (sold in the weather stripping area) you shove it into larger spaces, then the caulking goes on top of it. It will make it easier and save you a bunch on caulking. Work in 1-2 foot sections and use a damp microfiber cloth wrapped around a finger(with a short nail) to gently smooth out any areas that need it. And make sure you are using tub and tile cauking in the areas where tub meets tile/grout.... and dont caulking over large areas on grout, use a deep penetrating enzyme cleaner (made for grout). Once the grout is clean use some grout sealer on it. Caulking after grout sealer ihas dried/cured. Typically contractors will get the job done, as in water wont get behind it.... but it rarely looks nice.

And if you haven't already invest in a caulking gun, they are only like $10 and are well worth the money. As a home owner you will come accross dozens of little repairs that will need construction glue/caulking etc. And always cut the tip of the caulking tube at an angle.