Whats the best way to fill soul gems as an archer and a dual weilder? I have a bunch of empty soul gems... Do I have to equip a specific weapon or is there any easier way?

well you could always go the traditional way and get the spell soul trap , and just cast when enemy is about half hp. Or there are plenty of weps with soul trap as its proc.

Recently i found a dagger with a soul trap cast on it and once i had a bow with soul trap too. So if i was you i would enchant a weapon with a soul trap cast.
Perhaps your bow is the best choice for it .

I Carry a soul trapped bow in addittion to my regular one - just in case

I carry a soul trap sword with myself... I use it when i feel like trapping souls..

Conjuration and some perks that eventually allows all your summoned weapons to have soul trap. Just use your enchanted stuff until charge is low and then swap to some conjured weapons that fill your azuras star and use it to refill your enchanted stuff.

Or, get lots of money and buy soul gems around the place with souls in them.

Another way is to start using your Bound Sword/Axe and Bound Bow. Once you get to 30 Conjuration your Bound weapons will trap souls by default. Training up Conjuration with an Atronach will be easy for an Archer.

I carry:

Nightingale Bow
Nightingale Blade
Ebony arrows

And more importantly: DEMONFIRE

My ebony sword that is enchanted with the spell Soulfire. Which is a soul trap spell that also burns for 10pts. And that is 1 enchantment, I loves it.

This. My archer one shots basically everything, so it's the only way.

enchant soultrap on a dagger or better on the bow...i have that...works even too good (BILLIONS of soul gems in inventory)

I carry an extra bow with soul trap as well as an extra dagger/sword combo with it in case I need them. Try to find something like Fiery Soul Trap (an enchant which includes both Fire Damage and Soultrap in one...with the dual enchant perk you can slap say Frost on there as well, it's nasty) for your Soul Trap enchant, much more efficient than just Soul Trap, since the elemental damage is a nice bonus whether you can/want to ST the target or not.

Dagger with Soul Trap for 1 second. Get the backstab perk, and voila.

the good thing is, even with a small soulgem, with a 1sec souldtrap enchant (which is enough for 90% of sneak attacks) you can easily get well above 100 loads

Thanks guys

Put all your soul gems in a stack, and give them to a follower, and ensure they have a soul trap weapon. When your follower kills stuff, they will fill up a whole stack at a time unlike the player.

My Dunmer character carries a Daedric Bow with a strong soul trap enchant, and a Ebony Bow with no enchant. I also carry Black Star (reuseable Black soul gem) so I pick my targets carefully. I got my Archery skill to 100 and can pretty much one shot most foes with 'Soulsting'. I dual wield twin deadric swords and can take down most foes, but not sould trap them.

I preferr bow for soul trapping