Theory:

The other types of vegetative reproductions are fragmentation, fission (binary fission), budding and regeneration.
 
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Types of asexual reproduction: Clockwise from top left: Binary fission, Budding, Regeneration, and Fragmentation
Fragmentation:
The breaking of the filaments of filamentous algae into many fragments is known as fragmentation.
As each of these fragments contains atleast one cell, they grow up into a new filament of the algae by cell division.  Fragmentation occurs when the parent is matured enough. It is seen in Spirogyra.
 
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Fragmentation in spirogyra
Fission:
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Binary fission
  
In this mode of reproduction, the parent cell divides into two daughter cells, and each cell develops into a new adult organism.
It is seen in organisms like amoeba and bacteria.
Budding:
In this process, a daughter individual is formed from a small bulb-like projection on the parent body called a bud. The bud detaches from the parent body and forms a new daughter cell.
It is seen in organisms such as Yeast and Hydra.
 
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Budding in Yeast
  
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Budding in hydra
Regeneration:
The ability of an individual organism's lost bodily components to regenerate into a whole new organism is known as regeneration.
A specialised mass of cells carries it out.
It is observed in organisms such as Hydraand Planaria.
  
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Reference:
https://commons.wikimedia.org/wiki/File:Binary_Fission_2.svg
https://commons.wikimedia.org/wiki/File:Figure_43_01_02.jpg