You can get quite a few hall-effect sensors. These are quite easy to use and efficient. However, they are expensive and are not required if high accuracy/precision is not required.
You can use a regular resistor. It's called sense resistor because it is used for current sensing.
First you need to figure out resistance required. Then, you need to figure out required power.
What is the current level you are trying to measure and what is the voltage across it that you require?
You can use 0.1Ω, 0.01Ω, 0.001Ω, etc for current sensing, depending on required current sensing and power dissipation. I know that you can get down to 0.01Ω in the local market.
For selecting resistance and power rating, make use of the two equations:
V = I * R
P = \[{ I}^{2 }\] * R
Hope this helps.
Tahmid