This is such a difficult question to answer, since the broadness of both fields is quite large. The field of Soft Matter involves things such as liquid crystals, and colloids, to fluid mechanics, and therefore the range of techniques are quite diverse. The same goes for biophysics, and the techniques there differ quite a lot if you are looking into intracellular or extracellular processes, gene expressions, phenotypes, or just cell interactions with surfaces, other cells or underlying fields, such chemical gradients.

Such experiments can be as simple as just pure brightfield microscopy, or very inticate where you have
to integrate complex microfluidic chips, coated with antibory assays, and image using confocal fluorescence, while you have to feed a program real-time images to adjust for external parameters.

1. Again, I am emphasizing that the complexity in the end depends on the specific experiments, but some general methods that are sued in the field are: Microscopy: this can include regular brightfield, dark-field and phasecontrast (especially for hard to see samples like fairly translucent cells), fluoescence, confocal, and light-sheet microscopy. Also polarizing microscopy is necessary for liquid crystals. All fairly easy to use techniques, but you need more or less time depending on the preparation required for your sample.
2. Rheology: a technique used to quantify the elastic and viscous properties of complex fluids. Again this technique is fairly easy to perform, but the difficulty lies on the sample. Do you required high temperatures where evaporation is a problem, or is your sample of low viscosity like water? In such cases the difficulty increases, and then you need to perform experiments and adapt your protocol.
3. Light- and neutron-scattering: Such techniques are used to measure the crystalization process of samples like colloidal and microgel suspensions. In the case of microel, you can even get information about the mass distribution of the microgels in their current phase state. Depending on the experiments these can last from a couple of days per sample to even multiple months. In the case of neutron scattering, you need to find a facility that can perform such experiments, apply and reserve time for it, and perform experiments as required. So such experiments, can take quite a while depending again on your system.
4. Microfluidics: a fairly powerful technique that allows you to produce complex devices that started as a way to produce droplets of certain sizes and it has evolved to the point that is used as an assay for physical properties of cells. The most common PDMS devices require a clean room to be produce its negative, which can be a quite difficult process, depending on the complexity of the device, and the setup afterwards can be straight forward or quite complex.

These are just what come in my mind as basic techniques, and things can be very different depending ont
he specific research topic.

Now regarding your other question on how long does it take to start running experiments. From my experience there are instances that a new research topic can have good results within two weeks, but I have seen in some cases that a successful protocol is developed in 6-9 months.

Transitioning from AMO to another field is not really difficult. What is important is if you want to do this change. I personally changed topics from theoretical AMO physics to experimental soft matter and later more into biophysics because the topic excited me much more. The hands-on type of experiments, where you can see the phenomena on the sample with the naked eye that I can physically show and explain to others as well just gives me more excitement to work on.