After mRNA is released from the nucleus, the next process is its translation by ribosomes. By what physical, chemical or biochemical process does the mRNA reach the ribosome in the cytoplasm?
please have a look at this article and its images.
R. J. Jackson et al., 2010, Nature Rev. Mol. Cell Biol. 11:113.
In a nutshell, recognition of mRNA by ribosome occurs in multiple steps.Interaction of mRNA with (eukaryotic) initiation factors(eIF) leads to this. eIF4 complex interacts with mRNA and then an intermediate circular mRNA is formed with the aid of ATP hydrolysis.This circular mRNA attaches to the small subunit of ribosome.(the small subunit has a dozen of helper proteins attached to itself.) After the attachment of circular mRNA to the small subunit , you can say that mRNA has "found" the ribosome as the small subunit would then form a complex with the large subunit and begin the Elongation step of Translation.
The answer to the first part of your question is: diffusion. After transcription and some processing, the eukaryotic mRNA is exported to the cytoplasm. Here it floats around until it meets a ribosome. Binding of ribosome to mRNA is facilitated by proteins called initiation factors (IFs) and the 5' cap of mRNA$^1$.
The second part of your question basically asks about cell-free protein synthesis using an RNA template. This has already been shown to work: one is reminded of the famous Nirenberg–Matthaei experiment$^2$, which ultimately led to the cracking of the genetic code. Nirenberg and Matthaei worked with bacterial cell extracts, but systems based on eukaryotic cell extracts have also been developed$^3$.
References and further reading:
- Nelson DL, Cox MM. Lehninger principles of biochemistry. 7th ed (international edition). Basingstoke, England: Macmillan Higher Education; c2017. Chapter 27, Protein metabolism; p. 1077–1126.
- Nirenberg MW, Matthaei JH. The dependence of cell-free protein synthesis in E. coli upon naturally occurring or synthetic polyribonucleotides. PNAS. 1961 Oct 1;47(10):1588–1602. https://doi.org/10.1073/pnas.47.10.1588
- Chong S. Overview of cell‐free protein synthesis: historic landmarks, commercial systems, and expanding applications. Curr Protoc Mol Bio. 2014 Oct 1;108(1):16.30.1–11. https://doi.org/10.1002/0471142727.mb1630s108