I'd say that you just go through the ads (you can start here e.g. kv.ee/), find the property and contact the agency. It is very likely that at least one person in the agency speaks English and they'll take care of everything and give necessary advise. The peculiarity of Estonian real-estate market is that pretty much everything is handled via an agency. Estonians aren't fond of dealing with potential customers or lessees themselves and have the agencies deal with everything.
Yes, I can confirm, that our agencies organize everything. But one small recommendation - as there are many different agencies with different competency, it is always better to look at the status of the broker. On city24.ee - there is an "Atestated broker" status near the name and the yellow ring with the text "City24 kutseline kinnisvaramaalker" - it is in Estonian "Attested broker of City24". Just for example here city24.ee/realestate/flat/1023044 This is not very important but it gives a sense of extra security.
The prices have gone down in comparison with a couple of year ago situation. So now is is possible to buy property at the good/objective price. It is specially connected with the prices for the apartments in new houses (built in 2006 or later). As to the old apartments (houses buit in 1970 etc - the people mostly put too high price and do not want to give "discount", so these apartments cannot be sold during one year, and then the seller understands that his price was too high