Many types of extraction techniques can be applied starting from soxhlets, sonication,ASE and microwave. You can easily find those techniques and read about it and it may depends on the bioactive compound that you want to study.
You can use super critical carbon dioxide or subcritical water for extraction process, depending upon the type of compounds present. Use of organic solvents must be minimum.
Soxhlets, rotary vacuum extraction and over night soaking with solvent are the method to extract algae. Soxhlets and rotary vacuum extraction are boiling method some bio active compound are eliminate by heat so best method is over night soaking. At the same time some compound are dissolve in some boiling point so i use soxhlets, rotary vacuum extraction. So i suggest use this three method to extract the algae.
hope you can use some less toxic solvents,but really, it depends so much on polarity of your target compounds. Algae contain enzymes to quickly digest themselves to ugly smelly mess. If you could freeze-dry to a powder and then extract near liquid nitrtogen temp you might preserve the native bioactives. Best of luck! It is near and dear to my heart and grad school studies.