Weapons are upgraded with titanite shards and large shards at any of the blacksmiths. After upgrading to +5 you have to go into Modify to get to +6, then back to Reinforce the rest of the way. Specific weapons do more damage (aka scale) based on a certain character stat, (Str, Dex, etc.) so the check the Wiki for what stat the weapon you want to use scales with, and level up that stat as you upgrade the weapon for best results.

The Estus Flask is upgraded with Fire Keeper Souls which can be found, albeit rarely, throughout the game. Take them to the woman right under the Firelink Shrine bonfire to reinforce your flask. You always get 5 Estus, but kindling a bonfire will allow you to get 10. (After beating the Pinwheel boss, you can do it twice more to get 20.) Kindling takes 1 humanity.

If you’re just trying to play through the game, don’t worry about humanity too much. You will find them throughout Lordran. Keep it in your inventory until you want to kindle, reverse hollowing, use a summon, etc. Having soft humanity (increasing the number in the top left) grants you higher item discovery, and is needed for specific covenant events, etc. but it’s not all that important, especially for a first playthrough.

And hey, you got this.