It all needs to be scraped out, the surface needs to be scrubbed clean and then rinsed and left to dry completely.
Then (and only then) should new caulk be applied.
As for learning, internet videos have many examples of how to do it properly but there is some skill gained by experience. Each application method (squeeze tube vs. caulking gun) also involves slightly different skill-set and both have advantages and disadvantages.
I recommend that you use silicone (for durability, adhesion, and water-resistance); that you use a squeeze tube applicator (easier control for novice); and that you have mineral spirits handy in a small bucket along with several sacrificial rags. Use a finger dipped in mineral spirits to carefully smooth the caulk after application, and use the rags to clean any "oops" and to clean up any smeared caulk that got anywhere you didn't want it to be.
Even if it's not perfect in the end, it will look better and be more water-protective than the old crap that is there now... and you will learn a bit and your next caulk job will be easier.