How do balance transfers work?

I'm gonna guess the short answer is "depends on your card company" but I figured I should ask here before I start calling them. 

Lowe's credit card has upped their interest rate to 32% across the board. berkeley that. 

My current Barclays issued card is offering me 3% on balance transfers for a year. 

I'm still looking around to maybe get a 0%, but I also don't want yet another credit card. 

I know the big thing is to pay it off within that year, or else I'll get hit with accrued interest. Still, accrued interest would only be 15% instead of 32%.

But how does it work? Which company do I call first to initiate things? Does it count as the monthly payment or should I make a payment then do the transfer? Are there other questions I should be asking that I don't know about?

Call Barclays and when you call them, have your recent Lowes bill (or billing website) in front of you.  

Barclays is going to pay off your Lowes card.  You will no longer be indebted to Lowes and in exchange you will be indebted to Barclays for potentially less fee.  

In reply to John Welsh :

I didn't think it could be that simple. Thank you. 

You'll probably have to pay a transfer fee of 3%-5%. 

FYI Citi and Discover often offer balance transfers for 12 months at zero percent interest with 3-5% transfer fee. Both I have used and always able to do online. Super simple process.

Go to balance transfer offer and key in your account number of the one you want to transfer. Within a week or two they pay the balance. Just keep track of when it says your rate changes back so it's paid before you accrue additional interest. Depending on your billing cycle you may not need to make a payment until it's transferred a month out.

Look at nerdwallet.com 

You'll likely be able to find a card that will do an 18 month no interest transfer. If you haven't paid it off by then, find another card with 0 intersest transfer.