Tips
These are a few suggestions for things to make viewing the night sky more enjoyable. Remember, my advice is free and you get what you paid for...
GOLDEN RULE (and I can't stress this enough).
This is an old cliche, but is still the most important advice: "The best telescope for you is the one you will use the most" or to put it another way: "The easier it is to for you to go out and observe, the more you will do it".
This is the reason I use an 8-inch scope and don't really want anything bigger. Sure I could build or buy a 20-inch scope, and get much better views, but the actual number of times I'd use it would be small, due to the hassle of setting it up and waiting for the mirror to cool down, etc. I can look through other people's large scopes about as frequently as I would use one if I owned it. An 8-inch scope provides very pleasing views of enough objects to last a lifetime.
This is also the reason I custom build my scopes to contain everything I'm likely to need during an observing session (eyepiece storage, filter wheel, cupboard to store books, etc.). This means I can quickly and conveniently set up in a single trip, and am less likely to forget something crucial. With a bit of planning, you can develop your own procedures to suit you which will become second nature, and allow you to be observing comfortably in the shortest amount of time.
Lots of people use the phrase "aperture is King" and encourage people to buy the biggest telescope they can afford. I'd say that aperture is very important, but the best modification you can make to a scope is to take it to a really dark site. That's why it's important to have a scope you can easily transport. I much prefer observing with my 3.5" scope from the top of a very dark mountain site, than my 8-inch scope from my backyard or a fairly dark site! Again it's all a question of portability. If I had room to take a bigger telescope with me to The Andes, for example, then that would be better still!
General Tips
Keep a log! Make a note of the date and time you observed, a note of the sky conditions and a list of objects you looked at. At the very least, make a note of the objects you looked for (whether you managed to find them or not), how easy they were to find and what you thought of them. Having notes like this is very useful. For example, you might be looking back several months later, and think: "Oh, I couldn't find the Blue Snowball when I looked for it then, but now I can find it in about 30 seconds, and it's one of my favourites!" This gives you a record of how you're progressing, and will give you encouragement when you're convinced there's that one faint fuzzy you're never going to find. Having a list of your favourite objects gives you a very personal connection to the subject, and makes it easier to remember cool stuff to show other people. I use a shorthand method which makes note-taking very quick (which means I'm more likely to do it!). Wrap an elastic band around your book to mark the current page. This makes finding the right page much easier in the dark.
Observing Tips
Get dark adapted. In order to see faint objects, your eyes need to adjust to the low light levels. This can take some time. Various numbers are quoted like 30 mins - 1 hour in order to become fully dark adapted, but this probably depends on the individual and how dark your site is. I've found closing my eyes tightly for about 10 seconds, once outside, gives an instant improvement.
Drape a black cloth over your head. This gives the biggest improvement to your observing experience for the least outlay of money. Preventing stray light from entering your eyes means you can see fainter, and I really like the effect of not seeing anything at all except blackness and the stars in the eyepiece. It's almost equivalent to those really expensive wide-field "space-walk" eyepieces for a fraction of the cost. I like to use a black hood to completely immerse myself in the view through the eyepiece.
Stay dark adapted. The black hood only protects your night vision whilst looking through the eyepiece. In order to find the object, you need to look up at the sky. If nuisance light from neighbours/streetlights shines into your eye whilst you're searching, you're not going to be able to stay dark-adapted. A quick fix is to put up a screen around your observing area to prevent stray light from hitting you and your scope.
In addition to blocking other people's light, you have to be careful not to then destroy your night vision by producing too much light of your own! Use a dim red flashlight. There seems to be a common misconception that any red light is safe for your night vision. It's not! It must be the faintest light you can still usefully use. I recently bought a Rayovac head lamp after reading a suggestion on an astronomy forum that it was ideal for astronomy (the box even mentions the red light protects night vision) but it was way too bright, even after fairly heavy filtering. If you're using any computers or electronics, you have to be careful the display isn't too bright. I'm guilty of this myself, and the indicators on the switches for my 8-inch's electronics were much brighter than I expected, the first time I wired them up. The hand paddles I've seen on many GOTO scopes also seem ridiculously bright. If you're using a planetarium program on a laptop, the night vision mode (in which the screen goes dim and red) is probably still too bright. Many people recommend adding a neutral density filter or a sheet of rubylith (as used by printing companies).
Seeing fainter
In order to have the best possible chance of seeing that faint fuzzy, it pays to know exactly where you're looking. Make sure you have a good map of the area (either from a book, print-out, laptop screen, etc). Make sure the stars indicated on your map are roughly to the same depth as those you expect to see in your scope, and ensure you know your field of view. It helps to make a circular template sized to represent the field of view of your eyepiece on your map. You could use wire, or an overhead projector transparency, or I found a sheet of template plastic used by dressmakers in a fabric department, which was ideal.
Once you're looking in the right place, use averted vision. This extremely useful technique involves looking slightly away from the object so that you're actually looking at the object out of the corner of your eye. This part of your eye is more sensitive to low light levels. Tapping the tube of your scope also helps, as your eye is better able to distinguish an object if it is moving.
In order to get the most out of an object, it helps to sketch it. It doesn't have to be a work of art. The idea is that sketching forces you to look at the object in more detail and see features you didn't even know were there with just an initial glance. Your sketch also provides you with a permanent and personal record of your observations.
Make sure you're comfortable. Sitting comfortably really does allow you to see better! I recommend getting an observing chair where the height of the seat can be adjusted to fit your eyepiece height. One can be built easily within a weekend for ~CDN$30. The commercial ones are in the region of $CDN150, but for a bit less money a better chair can probably be found at a local guitar shop.