So the basic aspects of these combinations is the Entry and the Follow-up. Entry combinations consist of basic punches/kicks such as the jab, cross, elbow etc. The aim of Entry combinations is to set you up in order to effectively execute a Follow-Up combination.

Some sample Entry combinations are:
- Jab, Hook
- Jab, Overhand
- Jab, Jab
- Jab, Cross
Some sample Follow-up moves you can use to create your Follow-up combinations are:
- Hook
- Uppercut
- Overhand
- Elbow
- Low Kick
- Push Kick
The basic formula for creating your Muay Thai Combinations is to use one of the Entry combination, and add one or two Follow-up moves, such as:
- Jab, Hook, Elbow (Enter combinations are in this color, Follow-up combinations are in this color)
- Jab, Cross, Hook
- Jab, Jab, Overhand
- Jab, Jab, Hook, Elbow
- Jab, Elbow, Cross, Hook
- Jab, Cross, Overhand, Hook
- Jab, Cross, Elbow, Cross
- Jab, Jab, Low Kick, Elbow

You can mix and match and Entry combinations with any Follow-up moves, but remember that some combinations will flow better than others. Also, using more than two Follow-up moves in the same combination is an advanced technique and are difficult to execute.
Another point I want to mention is the Fakes. Fakes are basically a fake version of any of the Entry moves listed above, but done in a way as to confuse your opponent and set you up better for the Follow-up move. Here is an example taken from Youtube:
A demonstration of some more Muay Thai Combinations:
And another one: