There are times when I have to pick up items like Hextech Gunblade and/or Randuin's Omen, Maybe even pots. However, I'll forget to use them, be it in lane or in a team fight. The pots, not so much because I'm incredibly wary of my health, but in the middle of a team fight, I can't remember to active the items. Is there a good way to practice this?

Yes.. Try to look for oportune moments to use the item.. I used to have this issue with Zonyha's but now when u realize ur prob gonna die, cast that hourglass!!

The items are bounded by default to 123456 on the top row of numbers on the keyboard.
To help my fingers have to reach less, I ALWAYS move my active items to the first 3 slots in my inventory which corresponds to 123.

You just need to practice doing it, that's all. Start off buying one active item on one class a lot and get the hang of using it. (For example, I started off with tanky junglers or solo tops like Shen getting Randuin's Omen and got in the hang of taunting and popping Randuin's Omen in teamfights.

Different champs offer opportune ways to practice different item actives.

Morgana - Ult + zhonias combo
Skarner - shurelia's + ult combo
Lee Sin, Jax, Kat, etc - ward drop + escape skill
Malphite - ult + randuins combo
Akali - ult + gunblade combo

Heck, you can even practice using your actives on bots.

Same problem. Course when I realize I forgot the first time, I use it for the remainder of the match.

Like if I just finished building deathfire like three seconds ago, I generally forget to use it in the first team fight, realize I forgot, and then use it after that. Just force yourself to remember, it really helps.

Deathfire deals a percentage of the targets current HP as magic damage. It's base damage is 25% of their current HP, and it gains another 4% per 100 AP you have.