First of all overwrite all common files with the new ones. For example with unix shell cp -r obliquid-0.9.0/common/ obliquid-0.8.1/ or you can overwrite the common dir using ftp

Execute the following queries

INSERT INTO sl_configparms (name, setting, description, id_module, ord) VALUES ('cat3_group', '0', 'Id group to connect to category 3, 0 to use a custom category 3', 5, 40);
INSERT INTO sl_configparms (name, setting, description, id_module, ord) VALUES ('err_handling', 'none', 'Error handling one of (none, email, popup) Popup will be shown only if the user can see core/confpagegroup slot', 8, 5);

INSERT INTO sl_msg_text VALUES (84, 9, 'prj_prepare_invoice', 'en', 'Prepare invoice', 'The following phases have been closed, and an invoice should be prepared:\r\n\r\n{{foreach from=$p.phase item=ph}}Phase description:{{$ph}}\r\n{{/foreach}}Organization: {{$p.organization}}\r\nWork type: {{$p.activity}}\r\nBid code: {{$p.reference}}\r\nReport: {{$p.link}}\r\n\r\nClosed by: {{$p.name}}', '$p[organization] - Organization name
$p[activity] - Work type
$p[reference] - Bid Code
$p[phase] - An array of Phase descriptions
$p[link] - Link to the report screen
$p[name] - Name of person who closed the phase.', NOW(), 'Y');
INSERT INTO sl_msg_text VALUES (85, 9, 'prj_prepare_invoice', 'it', 'Preparare fattura', 'Le seguenti fasi sono state chiuse e bisogna fatturare:\r\n\r\n{{foreach from=$p.phase item=ph}}Descrizione fase:{{$ph}}\r\n{{/foreach}}Organizzazione: {{$p.organization}}\r\nTipo di lavoro: {{$p.activity}}\r\nCodice offerta: {{$p.reference}}\r\nCollegamento al sito: {{$p.link}}\r\n\r\nChiusa da: {{$p.name}}', '$p[organization] - Organizzazione
$p[activity] - Tipo di lavoro
$p[reference] - Codice offerta
$p[phase] - Un array con le descrizioni delle fasi
$p[link] - Collegamento al sito
$p[name] - Nome della persona che ha chiuso la fase.', NOW(), 'Y');

INSERT INTO sl_page VALUES ('core_javaedit',1,'Y','Enhanced text file editor, sends a message to people subscribed to core_edit on save');

INSERT INTO sl_slot (id_slot, id_module, slot, comment) VALUES (44, '1', 'javaedit', 'Enhanced text file editor, sends a message to people subscribed to core_edit on save');

INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (202, 'news_object', 'pos', 'integer', 0, 'N');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (200, 'news_text', 'pos', 'integer', 0, 'Y');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (201, 'news_text', 'blocklayout', 'integer', 0, 'N');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2550, 'news_cat', 'topic_images', 'text', 1, 'N');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2600, 'news_layout', 'id_news_layout', 'integer', 0, 'Y');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2601, 'news_layout', 'name', 'text', 80, 'N');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2700, 'prj_assigned', 'id_phase', 'integer', 0, 'Y');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2701, 'prj_assigned', 'id_person', 'integer', 0, 'Y');
INSERT INTO sl_tabledesc (id_tabledesc, tablename, field, type, length, is_primary) VALUES (2702, 'prj_assigned', 'id_project', 'integer', 0, 'Y');

ALTER TABLE `sl_news_object` ADD `pos` INT NOT NULL ;

ALTER TABLE `sl_news_text` ADD `pos` INT NOT NULL ,
ADD `blocklayout` INT NOT NULL ;

ALTER TABLE `sl_news_text` DROP INDEX `news_text` ;

ALTER TABLE `sl_news_text` ADD UNIQUE ( `id_news_item` , `lang` , `pos`);

ALTER TABLE `sl_news_cat` ADD `topic_images` CHAR( 1 ) NOT NULL ;

CREATE TABLE `sl_news_layout` (
  `id_news_layout` int(11) NOT NULL default '0',
  `name` char(80) NOT NULL default ''
) TYPE=MyISAM;

INSERT INTO `sl_news_layout` VALUES (1, 'Text on the left, photos on the right');
INSERT INTO `sl_news_layout` VALUES (2, 'Photos on the left, text on the right');
INSERT INTO `sl_news_layout` VALUES (3, 'Photos on top');
INSERT INTO `sl_news_layout` VALUES (4, 'Photos tiled horizontally on the left, text on the right');
    
CREATE TABLE `sl_prj_assigned` (
  `id_phase` int(11) NOT NULL default '0',
  `id_person` int(11) NOT NULL default '0',
  `id_project` int(11) NOT NULL default '0',
  UNIQUE KEY `id_prj_assigned_idx` (`id_phase`,`id_person`)
) TYPE=MyISAM;

Your upgrade should be now complete except for slot security to view the new additions. I suggest you to load some roles and assign them to groups