The analysis of the physical properties of low-redshift Ly$alpha$ emitters (LAEs) can provide clues in the study of their high-redshift analogues. At $z sim 0.3$, LAEs are bright enough to be detected over almost the entire electromagnetic spectrum and it is possible to carry out a more precise and complete study than at higher redshifts. In this study, we examine the UV and IR emission, dust attenuation, SFR and morphology of a sample of 23 GALEX-discovered star-forming (SF) LAEs at $z sim 0.3$ with direct UV (GALEX), optical (ACS) and FIR (PACS and MIPS) data. Using the same UV and IR limiting luminosities, we find that LAEs at $zsim 0.3$ tend to be less dusty, have slightly higher total SFRs, have bluer UV continuum slopes, and are much smaller than other galaxies that do not exhibit Ly$alpha$ emission in their spectrum (non-LAEs). These results suggest that at $z sim 0.3$ Ly$alpha$ photons tend to escape from small galaxies with low dust attenuation. Regarding their morphology, LAEs belong to Irr/merger classes, unlike non-LAEs. Size and morphology represent the most noticeable difference between LAEs and non-LAEs at $z sim 0.3$. Furthermore, the comparison of our results with those obtained at higher redshifts indicates that either the Ly$alpha$ technique picks up different kind of galaxies at different redshifts or that the physical properties of LAEs are evolving with redshift.