There are five individual types of tactic within Hattrick, listed with a brief explanation below. Fuller details can be found on the individual pages. Each tactic's effectiveness (except Play creatively) depends on certain skills of your players. Also, all of them have drawbacks that should be taken into consideration when using them.
Counter Attacks is a tactic which involves giving up midfield dominance in an attempt to score goals by counter-attacking. It can be very effective when used by a suitable team. This tactic is mostly chosen by defender trainers who have a very strong defense but a weak midfield. A team playing counter attacks takes a penalty of about 7% to its midfield rating compared to playing normal — note that the corresponding loss of possession will always be less than 1.81% (350/193% exactly).
Pressing means that all of your players try to put pressure on their opponents. They also put slightly more effort into breaking up your opponent's attacks than trying to create their own. The result is that the total number of potential chances in the game gets reduced for both teams. When you play pressing, all your players (except the goalkeeper) need excellent stamina and defending.
When using AIM, your team attempts to make more of your attacks down the centre of the pitch, at the expense of attacks on the wings. In other words, you trade attacks down the wings for attacks through the centre. You get a straight one for one exchange, so the total number of attacks remains constant. The disadvantage of this tactic is that your defence becomes somewhat worse.
The rules also mention that the percentage of gaining extra attacks can increase as much as 40%. This rating is calculated for each player in middle, by using their passing skills as a starter point. Referring to the manual on the main site.
This works in the same way as AIM, only in reverse. Instead of more attacks coming in the center, you get more of your attacks on the wings. Similarly to AIM, the disadvantage is that it weakens your central defence.
When you use Play Creatively, there is a greater chance that special events (both positive and negative) will occur for both teams during the match. If both teams use Play Creatively, the chance for special events will become even higher. Teams playing creatively will be less focused on the defence, thus losing some defensive ability. Playing creatively will probably be good for SE-optimized teams (i.e. for teams that have many players with specialties).
Recommended reading: ABC of Tactics