Well, you “leave it behind” in the sense that whatever you do with it, it’s untouchable until you’re retirement age unless you really want to make a BAD financial decision: if you withdraw it early, the government takes 10% in addition to charging taxes. So for example if you’re in a 28% federal tax bracket right now and your state charges 5% income tax, you’re out 33% plus that 10% so you’re out 43% of that money if you withdraw it. However as others have said, you do maintain ownership of it and can control how it’s invested.
IIRC, if the total of your account is small enough (3K or so?) the employer can decide that you have to take it with you - but that just means rolling it into an IRA or a new employer’s 401(k).
Always put at least enough into the 401(k) to get the employer’s match - if you don’t you’re leaving free money on the table.
More general stuff:
Try keeping track of every penny you spend - it can really help you see where the nickels and dimes go, and get a better handle on that sort of spending.
We use Quicken religiously for managing all our finances. MS Money is also supposed to be decent. Quicken tracks all of our retirement accounts, checking, other investments, so we have a very good handle on what we’re spending and what we own. It has a budgeting feature.
Columnist Michelle Singletary (Washington Post, Sundays and Thursdays) is chock-full of financial common sense. Her column, “The Color Of Money” may have been originally targeted at educating people of color (hence the title; she herself is African-American) but it’s sensible stuff for everyone. Her car advice: “buy used, and keep it until you’ve got your mechanic on speed dial”. Well, we usually buy new… but we only traded our last car (last year) when it let me down in Canada, followed by 2 months of constant problems; the day I phoned the shop - from memory - after I finally got it to start after work, I started shopping for a new car. We kept the old one 10 years, our other car is nearly 9 years old, and we’re hoping for a few more years on it, so we’re following part of her advice 
On the joint vs. yours-mine money philosophy: Singletary always insists “it’s JOINT money once you marry”. Well, that may not work for everyone but I think in general it’s good - one partner will nearly always have a bigger income than the other. We pool all the money. Though I do maintain a separate checking account, I just have “spending cash” transferred there once a month that I use for walking-around money and the occasional bill. That’s an approach that may work for you.
Oh - and I also personally recommend that each person have one account of some sort independent of the other. That way if something happens, you’ve still got access to some funds. I misplaced my wallet once a few years back - the last working day before the Christmas holiday. We were due to travel and I could not get replacement credit cards before the trip. Fortunately, my husband had his own Mastercard, and we were able to use that for the trip (since of course I’d cancelled all the cards in my wallet).