MIH, don't be sure they are low. A lot of people are so used to seeing overinflated tires that they think they are low when they are properly inflated. Anyway, you will need a gauge, but the air hoses at most gas stations already have one (though sometimes of uncertain accuracy). If you use the one attached to the air hose, it won't take a reading until you stop holding the lever to inflate, so just stop every so often and take a reading. If the correct pressure range isn't stamped right on your tires, check for a sticker inside one of the doors that may have that information. Otherwise, call whoever sold you the tires for the correct inflation pressure (it's usually somewhere between 28 and 32 psi, but will depend on the type of tire).
You can pick one of those gauges up in any auto parts store, or places like Sears (and probably a lot more places than that). They aren't very expensive or anything (though mine was given to me as a gift, so I don't really know how much they cost).
As for getting the air hose to inflate rather than deflate the tire, it's just a matter of keeping the hose pressed to the tire valve firmly, same with taking the tire pressure, push the gauge on firmly or you won't get an accurate reading.
It would be ridiculously silly to pay someone just to put air in the tires. You'll definitely be able to do this on your own.
As for checking the oil, do you have the manual that came with your car? It should have information of which dipstick is for the oil. There are some other dipsticks under the hood, so you want to be sure you're reading the right one. If you're not sure, next time you bring in your car for an oil change, ask to be shown so you can check the oil between visits. Once you know which is the dipstick, pull it out, wipe it off with a paper towel or rag, reinsert it completely, and pull it out again to take the reading. There will be a hatched area with arrows pointing to it to indicate where "full" is. Good, clean oil is fairly clear, maybe only a tad darker than cooking oil, if the oil on your dipstick is dark or black, get an oil change ASAP. If it's clean and just needs to be topped up, again, refer to your manual to make sure you add the oil to the right place...there is probably a symbol on the cap to let you know it's the one for oil, but double check so you don't do something silly like put oil in your brake fluid or windshield washer reservoir (or if you use one of those 15 min oil change type places, most of them will top up the oil for free if you need it before you've reached your 3000 mile recommended time for changes).