Basically ther are two types, they are 
1. Static Testing Technique
2. Dynamic Testing Technique

Static Testing Technique: 
             Testing without executing the program or a 
module. Static testing is of diffent types, they are 
Reviews.
Review is of two types 1. Formal Review and Informal Review
and Inspection, Walkthroughs, Desk checking, Peer rviews, 
Proof Reading comes under Reviews
Desk Checking,Proof Reading, Peer review are Informal 
Reviews
Inspection is Formal Review
Walkthrough can be both formal and informal

Dynamic Testing Technique: 
             Testing with executing the program or a module.
there are four different types. They are
1. Boundary Value Anlysis.
2. Equivalence Partitioning
3. Decision Table.
4. State Transition

The Testing strategies are mainly two types

1.WBT (White Box Testing) done by the developers
  A)Unit Testing

  B)Integration Testing

2.BBT (Black Box Testing) done by the testers
  C)Syetem Testing
    i) Usability Testing
   ii) Availablity Testing
  iii) Configuration Testing
   iv) Compatability Testing
    v) Performance Testing
        a) Stress Testing
        b) Load Testing
        c) Recovery Testing
   vi) Maintainbility Testing
       a)Corrective Maintenance
       b)Perfective Maintenance
       c)Adaptive Maintenance
  vii) Reliability Testing
 viii) Accessibility Testing
   ix) Installation Testing

  D)User Acceptance Testing
    i) Alpha Testing
   ii) Beta Testing

There are many others kinds of Testing...those are not 
mandatory for all companies...these are

1. Positive Testing
2. Negative Testing
3. Smoke Testing
4. Sanity Testing
5. Monkey Testing
6. Gorilla Testing
7. Database Testing
8. OperationalTesting
9. Post-Mortem Testing
10.Ad-Hoc Testing
11.Error Guessing
12.Localization Testing
13.Internationalization Testing 
14.Gray Box Testing
15.GUI Testing  etc..................