Some hints as I think of them.

Lower your resolution

Use Ctrl-Alt-+ and Ctrl-Alt-- to lower the resolution so you can easily read specials in your opponents well.

Don't bother trying to get multiple rows out at once

It's a bigger goal to keep your well empty. A small well has a higher concentration of specials, and is safer from attack. A more full well is more vunerable to people playing specials on you. If you wait for a piece that is needed to remove multiple rows from your well you will only end up building your well higher.

Don't build towers

It's tempting to place blocks one on top of each other to avoid covering holes and thus having a huge tower. This is a very vunerable position in tetrinet as most specials will ruin your nice new tower and will prevent you getting rows out, and someone getting a few rows out will of course push your tower up. Remember, if any block goes over the top of your well, it's game over.

Specials

Try and collect as many specials as possible

Try and fill your inventory with good specials. You really want to have at least one nuke field/switch field or block gravity in your inventory at once. If you have worthless or minor specials (such as clear specials) try and play them to keep your inventory open for better specials.

Hold offensive specials in reserve for blizkreigs

It's far more damaging to play all your specials in one go than to play them one at a time, and if you play them all at once hopefully your opponent won't get a chance to retaliate.

Block quake (Q)

Play this special on your opponent who has the most structured, highest well. It will push the rows around making large column holes disappear making it harder for them to clear rows. Playing multiple of these on a single player is adventagious.

Block Bomb (O)

Play this only on an opponent who has an O in their well, otherwise it has no effect. This is a very cruel attack, especially if followed up with a few add rows. If this is in your well you should spend your time trying to get rid of it, either by removing the row, or, if thats impossible, by using a "Clear row" special.

Clear Row (C)

Removes a row from the bottom of the well. Play this if you have an O special in the bottom of your well and you can't get to it to remove it yourself, or if you have no specials in the bottom of your well, or your well is getting too high. Try and play these regularly as it will keep your well low giving you a higher density of specials and keeps your inventory clear for other specials.

Add Row (A)

Keep these in reserve and play them on people who's well are near the top, preferably in quick succession. The goal is to push that player out of the game in one fatal blow.

Clear Specials (b)

Removes all specials from a well. Usually an offensive weapon, but can be played on yourself to get rid of a Block Bomb. Consider playing this on people with lots of specials in their well, preferably if they are about half way up their well (people lower in the well are likely to get their specials back by getting rid of rows, people higher are unlikely to get to the specials they have). Don't play this on opponents who have a block bomb, you want to leave them vunerable to block bomb attacks.

Switch Field (S)

Lets you swap a field with another player. Usually you wait until your well is pretty well buggered then screw it up some more (perhaps with some Add Rows) or just dropping blocks in awkward places and then swapping with an opponent. Try and swap with an opponent who has the lowest well. Tetrinet will clearline on switch if the well is actually completely full, and you want to leave yourself some breathing room if they have a switch field to switch field back.

Nuke Field (N)

Clears out the entire well. Play it on yourself. Wait until you're almost dead then play it, bewary of opponents having a switch field and soon after switching fields with you and stealing your hard earnt nice clean well.

Block Gravity (g)

Condenses your blocks vertically down to eliminate any spaces. Usually results in lots of rows and specials. This is a godsend if you have just been block bombed.

Clear Random (r)

Clears a few random blocks from the field. Good for annoying people who are building towers. Play multiple for better effect.