The adjustable cup can be adjusted with an adjustable wrench or regular open-wrench set. If they are too thick and you don't want to take off your crank arm, you might need to get a cone wrench.
And while you can tighten the lock ring with the screwdriver tip, I find that this has a tendency to cause damage to the lock ring.
One of the joys of doing your own work is accumulating cool new toys.. err.. tools. So I'd splurge and get the proper tool. Cone wrenches are pretty cheap.
The lock ring wrench is a little more expensive. Here is the cheapo version, XLC Adjustable Bottom Bracket Spanner ($5-8):
XLC Adjustable Bottom Bracket Spanner2
Your local bike shop can provide you with options and make sure you get the right wrenches or you can shop at a discount bike parts shop. There are very good tips on how to adjust your bottom bracket at Sheldon Brown's site: http://www.sheldonbrown.com/tooltips/bbadj.html