I geocache without a GPS (just because I haven't been able to get one as of yet!)...but it can be very exciting to find one just using a map and some instinct...heres what I do...
1) I am still very very new to this so I start with caches with difficulty ratings of 1-2
2) I read the description of the cache as well as the logs...
3) click the link (map) that takes you to mapquest to see where it is...in general, and note cross streets, names of parks etc...
4) Then I go to Lost Outdoors and type the coordinates found on the top of the mapquest page (lat and long) into the area for the map on the lost outdoors site...click 'make map' and you have an aerial view of the cache...
If, from there, it looks like something you should be able to find...using some noticable landmarks, then go for it! I usually look for distance from the closest street, sidewalk, cluster of bushes/trees, any clearings nearby?...how far from these things is the red dot?...it's worked out pretty well for me
If you can't seem to find it, then decrypt the hint...that usually gets you right to it!
Good luck...
SixTen